Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 129 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. #5579 | C2 | semidirect |
| 2. C3×#446 | C2 | semidirect |
| 3. #4847 | C2 | semidirect |
| 4. #4847 | C2 | semidirect |
| 5. #4846 | C2 | semidirect |
| 7. #4702 | C2 | semidirect |
| 9. #4683 | C2 | semidirect |
| 42. #446 | D3 | semidirect |
| 69. D24 | Q8 | semidirect |
| 188. C3 | #3389 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5579 | 2 |
| C3×#446 | 2 |
| #4847 | 2 |
| #4846 | 2 |
| #4711 | 2 |
| #4702 | 2 |
| C4×D24 | 2 |
| #4683 | 2 |
| #3389 | 3 |