Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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. #5542 | C2 | semidirect |
| 4. #5019 | C2 | semidirect |
| 5. #4873 | C2 | semidirect |
| 6. #4767 | C2 | semidirect |
| 7. #4699 | C2 | semidirect |
| 8. C8×Dic6 | C2 | semidirect |
| 164. C3 | #3393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5542 | 2 |
| C3×C4×D8 | 2 |
| #5155 | 2 |
| #5019 | 2 |
| #4873 | 2 |
| #4767 | 2 |
| #4699 | 2 |
| C8×Dic6 | 2 |
| #3393 | 3 |