Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 133 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×#904 | C2 | semidirect |
| 2. #5551 | C2 | semidirect |
| 3. C3×C8×D4 | C2 | semidirect |
| 4. #5116 | C2 | semidirect |
| 5. #4841 | C2 | semidirect |
| 6. #4733 | C2 | semidirect |
| 7. #4699 | C2 | semidirect |
| 8. C4×D24 | C2 | semidirect |
| 37. C8×D4 | D3 | semidirect |
| 62. D24 | D4 | semidirect |
| 140. C3×C4 | #135 | semidirect |
| 182. C4 | #904 | semidirect |
| 185. C3 | #3283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| #5551 | 2 |
| C3×C8×D4 | 2 |
| #5116 | 2 |
| #4841 | 2 |
| #4733 | 2 |
| #4699 | 2 |
| C4×D24 | 2 |
| #3283 | 3 |