Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
696 conjugacy classes of subgroups; only the 325 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 325 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C4×Dic3⋊C4 | C2 | semidirect |
| 7. #4649 | C2 | semidirect |
| 15. C2×Dic3⋊C4 | C4 | semidirect |
| 22. #877 | C4 | semidirect |
| 51. Dic3⋊C4 | C2×C4 | semidirect |
| 54. C4×Dic3 | C2×C4 | semidirect |
| 89. C2×Dic3 | C42 | semidirect |
| 173. C3 | #2274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic3⋊C4 | 2 |
| C2×#877 | 2 |
| C3×C4×C22⋊C4 | 2 |
| C4×#217 | 2 |
| Dic3×C22⋊C4 | 2 |
| C4×Dic3⋊C4 | 2 |
| #4649 | 2 |
| #2274 | 3 |