Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
456 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×C3×C4×C8 | C2 | semidirect |
| 3. #5115 | C2 | semidirect |
| 4. #4695 | C2 | semidirect |
| 5. #4694 | C2 | semidirect |
| 6. C4×D24 | C2 | semidirect |
| 7. #4682 | C2 | semidirect |
| 31. C2×C4×C8 | D3 | semidirect |
| 74. C2×C3×C4 | D8 | semidirect |
| 89. C3×C8 | #41 | semidirect |
| 137. C2×C4 | D24 | semidirect |
| 145. C8 | #235 | semidirect |
| 165. C3 | #3169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5477 | 2 |
| C2×C3×C4×C8 | 2 |
| #5115 | 2 |
| #4695 | 2 |
| #4694 | 2 |
| C4×D24 | 2 |
| #4682 | 2 |
| #3169 | 3 |