Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
58 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #6198 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #6196 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #6188 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×(C3⋊D3)⋊C3 | — | 2 | 1 | no | — |
| 5 | #1084 | C22 | 1 | 1 | yes | characteristic |
| 6 | (C3⋊Dic3)⋊C3 | — | 2 | 1 | no | — |
| 7 | #627 | — | 6 | 1 | no | — |
| 8 | #626 | — | 6 | 1 | no | — |
| 9 | C2×H(3,𝔽3) | D4 | 1 | 1 | yes | characteristic |
| 10 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 11 | #204 | — | 9 | 1 | no | maximal |
| 12 | C2×C3⋊D3 | — | 2 | 1 | no | — |
| 13 | C2×C3×D3 | — | 6 | 1 | no | — |
| 14 | C3⋊Dic3 | — | 2 | 1 | no | — |
| 15 | C3×Dic3 | — | 6 | 1 | no | — |
| 16 | C3×Dic3 | — | 6 | 1 | no | — |
| 17 | C3×Dic3 | — | 6 | 1 | no | — |
| 18 | H(3,𝔽3) | SD16 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 19 | #67 | — | 18 | 1 | no | — |
| 20 | D12 | — | 9 | 1 | no | — |
| 21 | Dic6 | — | 9 | 1 | no | — |
| 22 | Dic6 | — | 18 | 1 | no | — |
| 23 | C3×C8 | — | 9 | 1 | no | — |
| 24 | C2×C32 | — | 2 | 1 | no | — |
| 25 | C2×C32 | — | 2 | 1 | no | — |
| 26 | C3⋊D3 | — | 4 | 1 | no | — |
| 27 | C3×D3 | — | 12 | 1 | no | — |
| 28 | SD16 | — | 27 | 1 | no | Sylow |
| 29 | C22×C3 | — | 18 | 1 | no | — |
| 30 | C2×D3 | — | 6 | 1 | no | — |
| 31 | C2×D3 | — | 36 | 1 | no | — |
| 32 | C3×C4 | — | 9 | 1 | no | — |
| 33 | C3×C4 | — | 18 | 1 | no | — |
| 34 | Dic3 | — | 6 | 1 | no | — |
| 35 | Dic3 | — | 6 | 1 | no | — |
| 36 | Dic3 | — | 6 | 1 | no | — |
| 37 | Dic3 | — | 36 | 1 | no | — |
| 38 | C32 | — | 2 | 1 | no | — |
| 39 | C32 | — | 2 | 1 | no | — |
| 40 | Q8 | — | 27 | 1 | no | — |
| 41 | D4 | — | 27 | 1 | no | — |
| 42 | C8 | — | 9 | 1 | no | — |
| 43 | C2×C3 | — | 12 | 1 | no | — |
| 44 | C2×C3 | — | 12 | 1 | no | — |
| 45 | C2×C3 | — | 36 | 1 | no | — |
| 46 | C2×C3 | GO+(4,𝔽2) | 1 | 1 | yes | characteristic |
| 47 | D3 | — | 12 | 1 | no | — |
| 48 | D3 | — | 36 | 1 | no | — |
| 49 | C22 | — | 18 | 1 | no | — |
| 50 | C4 | — | 9 | 1 | no | — |
| 51 | C4 | — | 18 | 1 | no | — |
| 52 | C3 | — | 12 | 1 | no | — |
| 53 | C3 | — | 12 | 1 | no | — |
| 54 | C3 | #3775 | 1 | 1 | yes | characteristic |
| 55 | C2 | — | 36 | 1 | no | — |
| 56 | C2 | #1088⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #6196 | C2 | semidirect |
| 3. #6188 | C2 | semidirect |
| 18. H(3,𝔽3) | SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #6198 | 2 |
| #6196 | 2 |
| #6188 | 2 |
| #204 | 9 |