Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
352 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 352 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. #5579 | C2 | semidirect |
| 2. C3×C8×Q8 | C2 | semidirect |
| 3. #4847 | C2 | semidirect |
| 4. #4842 | C2 | semidirect |
| 7. #4683 | C2 | semidirect |
| 8. #4682 | C2 | semidirect |
| 34. C8×Q8 | D3 | semidirect |
| 56. D24 | Q8 | semidirect |
| 158. C3 | #3380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5579 | 2 |
| C3×C8×Q8 | 2 |
| #4847 | 2 |
| #4842 | 2 |
| C4×D24 | 2 |
| #4683 | 2 |
| #4682 | 2 |
| #3380 | 3 |