Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 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. #5555 | C2 | semidirect |
| 2. C3×C8×D4 | C2 | semidirect |
| 3. #5115 | C2 | semidirect |
| 4. C2×#818 | C2 | semidirect |
| 5. #4846 | C2 | semidirect |
| 6. #4736 | C2 | semidirect |
| 7. C4×D24 | C2 | semidirect |
| 8. #4682 | C2 | semidirect |
| 35. C8×D4 | D3 | semidirect |
| 80. C3×D4 | D8 | semidirect |
| 97. C3×C8 | #41 | semidirect |
| 140. D4 | D24 | semidirect |
| 153. C8 | #237 | semidirect |
| 173. C3 | #3334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5555 | 2 |
| C3×C8×D4 | 2 |
| #5115 | 2 |
| C2×#818 | 2 |
| #4846 | 2 |
| #4736 | 2 |
| C4×D24 | 2 |
| #4682 | 2 |
| #3334 | 3 |