Finite Group DatabasebetaFinite Group DatabasebetaOrder 144.
114 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×C32×C4 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C3⋊Dic3 | C2 | 1 | 2 | yes | maximal |
| 3 | #634 | C2 | 1 | 4 | yes | maximal, direct product factor |
| 4 | C2×Dic6 | — | 3 | 4 | no | maximal |
| 5 | C22×C32 | C22 | 1 | 1 | yes | characteristic |
| 6 | C32×C4 | C22 | 1 | 2 | yes | — |
| 7 | C3⋊Dic3 | C22 | 1 | 4 | yes | — |
| 8 | C2×C3×C4 | D3 | 1 | 4 | yes | — |
| 9 | C2×Dic3 | — | 3 | 8 | no | — |
| 10 | Dic6 | — | 3 | 16 | no | — |
| 11 | C2×C32 | Q8 | 1 | 2 | yes | complemented |
| 12 | C2×C32 | C23 | 1 | 1 | yes | characteristic |
| 13 | C2×Q8 | — | 9 | 1 | no | Sylow |
| 14 | C22×C3 | C2×D3 | 1 | 4 | yes | — |
| 15 | C3×C4 | C2×D3 | 1 | 8 | yes | — |
| 16 | Dic3 | — | 3 | 16 | no | — |
| 17 | C32 | C2×Q8 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 18 | Q8 | — | 9 | 4 | no | — |
| 19 | C2×C4 | — | 9 | 2 | no | — |
| 20 | C2×C4 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 21 | C2×C3 | Dic6 | 1 | 8 | yes | complemented |
| 22 | C2×C3 | C22×D3 | 1 | 4 | yes | — |
| 23 | C22 | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 24 | C4 | — | 9 | 4 | no | — |
| 25 | C4 | C2×C3⋊D3 | 1 | 2 | yes | — |
| 26 | C3 | C2×Dic6 | 1 | 4 | yes | complemented |
| 27 | C2 | #634 | 1 | 2 | yes | direct product factor |
| 28 | C2 | C22×C3⋊D3 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #634 | C2 | direct (N × H) |
| 11. C2×C32 | Q8 | semidirect |
| 17. C32 | C2×Q8 | semidirect |
| 21. C2×C3 | Dic6 | semidirect |
| 26. C3 | C2×Dic6 | semidirect |
| 27. C2 | #634 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4 | 2 |
| C2×C3⋊Dic3 | 2 |
| #634 | 2 |
| C2×Dic6 | 3 |