Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 1. C2×#909 | C2 | semidirect |
| 3. C2×C4×Dic6 | C2 | semidirect |
| 4. C3×#423 | C2 | semidirect |
| 5. #5133 | C2 | semidirect |
| 6. #4849 | C2 | semidirect |
| 7. #4848 | C2 | semidirect |
| 8. #4845 | C2 | semidirect |
| 41. #423 | D3 | semidirect |
| 57. C2×Dic6 | D4 | semidirect |
| 178. C3×C4 | #137 | semidirect |
| 232. C4 | #909 | semidirect |
| 235. C3 | #3037 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#909 | 2 |
| #5477 | 2 |
| C2×C4×Dic6 | 2 |
| C3×#423 | 2 |
| #5133 | 2 |
| #4849 | 2 |
| #4848 | 2 |
| #4845 | 2 |
| #3037 | 3 |