Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. D4×Dic6 | C2 | semidirect |
| 4. C3×#436 | C2 | semidirect |
| 5. #5137 | C2 | semidirect |
| 6. #4849 | C2 | semidirect |
| 7. #4841 | C2 | semidirect |
| 8. #4739 | C2 | semidirect |
| 9. #4733 | C2 | semidirect |
| 10. #4699 | C2 | semidirect |
| 11. C4×#204 | C2 | semidirect |
| 53. #436 | D3 | semidirect |
| 93. #204 | D4 | semidirect |
| 203. C3×C4 | #137 | semidirect |
| 260. C4 | #909 | semidirect |
| 263. C3 | #3276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#909 | 2 |
| #5551 | 2 |
| D4×Dic6 | 2 |
| C3×#436 | 2 |
| #5137 | 2 |
| #4849 | 2 |
| #4841 | 2 |
| #4739 | 2 |
| #4733 | 2 |
| #4699 | 2 |
| C4×#204 | 2 |
| #3276 | 3 |