Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
410 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 410 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. #5479 | C2 | semidirect |
| 2. #5477 | C2 | semidirect |
| 3. C2×C3×#97 | C2 | semidirect |
| 4. #5115 | C2 | semidirect |
| 5. #5114 | C2 | semidirect |
| 6. #4714 | C2 | semidirect |
| 7. #4713 | C2 | semidirect |
| 8. #4712 | C2 | semidirect |
| 9. #4711 | C2 | semidirect |
| 10. #4710 | C2 | semidirect |
| 11. #4702 | C2 | semidirect |
| 54. C2×#97 | D3 | semidirect |
| 153. C3×C8 | #41 | semidirect |
| 241. C8 | #235 | semidirect |
| 268. C3 | #3180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5479 | 2 |
| #5477 | 2 |
| C2×C3×#97 | 2 |
| #5115 | 2 |
| #5114 | 2 |
| #4714 | 2 |
| #4713 | 2 |
| #4712 | 2 |
| #4711 | 2 |
| #4710 | 2 |
| #4702 | 2 |
| #3180 | 3 |