Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
446 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 446 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. #5477 | C2 | semidirect |
| 2. C3×C4×M16 | C2 | semidirect |
| 3. #5135 | C2 | semidirect |
| 4. #4711 | C2 | semidirect |
| 5. #4695 | C2 | semidirect |
| 6. #4694 | C2 | semidirect |
| 7. #4680 | C2 | semidirect |
| 31. C4×M16 | D3 | semidirect |
| 84. C3×C8 | #41 | semidirect |
| 132. C8 | #235 | semidirect |
| 148. C3 | #3184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5477 | 2 |
| C3×C4×M16 | 2 |
| #5135 | 2 |
| #4711 | 2 |
| #4695 | 2 |
| #4694 | 2 |
| #4680 | 2 |
| #3184 | 3 |