Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
482 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 131 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×C3×#135 | C2 | semidirect |
| 2. #5831 | C2 | semidirect |
| 3. C2×D3×Q16 | C2 | semidirect |
| 4. #5239 | C2 | semidirect |
| 5. Dic3×Q16 | C2 | semidirect |
| 6. #5170 | C2 | semidirect |
| 7. #5166 | C2 | semidirect |
| 8. #5157 | C2 | semidirect |
| 9. #5155 | C2 | semidirect |
| 10. #5116 | C2 | semidirect |
| 11. C8×#67 | C2 | semidirect |
| 42. C2×#135 | D3 | semidirect |
| 68. C3×Q16 | D4 | semidirect |
| 169. Q16 | #67 | semidirect |
| 200. C2×D3 | #135 | semidirect |
| 266. C3 | #3285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#135 | 2 |
| #5831 | 2 |
| C2×D3×Q16 | 2 |
| #5239 | 2 |
| Dic3×Q16 | 2 |
| #5170 | 2 |
| #5166 | 2 |
| #5157 | 2 |
| #5155 | 2 |
| #5116 | 2 |
| C8×#67 | 2 |
| #3285 | 3 |