Finite Group DatabasebetaFinite Group DatabasebetaOrder 96.
38 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×Dic6 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×M16 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #208 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #101 | — | 3 | 1 | no | maximal, Sylow |
| 5 | C2×C3×C4 | C22 | 1 | 1 | yes | characteristic |
| 6 | C2×Dic3 | C4 | 1 | 2 | yes | — |
| 7 | Dic6 | — | 2 | 1 | no | — |
| 8 | Dic6 | — | 2 | 1 | no | — |
| 9 | C3×C8 | — | 2 | 1 | no | — |
| 10 | C3⋊C8 | — | 2 | 1 | no | — |
| 11 | C2×Q8 | — | 3 | 1 | no | — |
| 12 | M16 | — | 3 | 1 | no | — |
| 13 | M16 | D3 | 1 | 1 | yes | characteristic |
| 14 | C22×C3 | C2×C4 | 1 | 1 | yes | characteristic |
| 15 | C3×C4 | D4 | 1 | 1 | yes | characteristic |
| 16 | C3×C4 | D4 | 1 | 1 | yes | characteristic |
| 17 | Dic3 | — | 2 | 2 | no | — |
| 18 | Q8 | — | 6 | 1 | no | — |
| 19 | Q8 | — | 6 | 1 | no | — |
| 20 | C2×C4 | — | 3 | 2 | no | — |
| 21 | C2×C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 22 | C8 | — | 2 | 1 | no | — |
| 23 | C8 | — | 6 | 1 | no | — |
| 24 | C2×C3 | — | 2 | 1 | no | — |
| 25 | C2×C3 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 26 | C22 | C4×D3 | 1 | 1 | yes | characteristic |
| 27 | C4 | — | 6 | 2 | no | — |
| 28 | C4 | D12 | 1 | 1 | yes | characteristic |
| 29 | C4 | #67 | 1 | 1 | yes | characteristic |
| 30 | C3 | #101 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 31 | C2 | — | 2 | 1 | no | — |
| 32 | C2 | (C2×D3)⋊C4 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 30. C3 | #101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic6 | 2 |
| C3×M16 | 2 |
| #208 | 2 |
| #101 | 3 |