Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #5522 | C2 | semidirect |
| 3. #5139 | C2 | semidirect |
| 4. C2×#825 | C2 | semidirect |
| 5. #5006 | C2 | semidirect |
| 6. C3×#344 | C2 | semidirect |
| 7. #4555 | C2 | semidirect |
| 17. #909 | C4 | semidirect |
| 19. #908 | C4 | semidirect |
| 35. #344 | D3 | semidirect |
| 49. C2×D12 | C2×C4 | semidirect |
| 54. C2×Dic6 | C2×C4 | semidirect |
| 59. C3×M16 | C2×C4 | semidirect |
| 160. M16 | C4×D3 | semidirect |
| 252. C3 | #1906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5748 | 2 |
| #5522 | 2 |
| #5139 | 2 |
| C2×#825 | 2 |
| #5006 | 2 |
| C3×#344 | 2 |
| #4555 | 2 |
| #1906 | 3 |