Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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. #5577 | C2 | semidirect |
| 2. C3×C8×Q8 | C2 | semidirect |
| 3. #4843 | C2 | semidirect |
| 4. #4695 | C2 | semidirect |
| 5. C4×D24 | C2 | semidirect |
| 21. C8×Q8 | D3 | semidirect |
| 49. C3×Q8 | D8 | semidirect |
| 60. C3×C8 | #41 | semidirect |
| 85. Q8 | D24 | semidirect |
| 96. C8 | #239 | semidirect |
| 110. C3 | #3391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5577 | 2 |
| C3×C8×Q8 | 2 |
| #4843 | 2 |
| #4695 | 2 |
| C4×D24 | 2 |
| #3391 | 3 |