Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
436 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 137 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. #4846 | C2 | semidirect |
| 5. #4843 | C2 | semidirect |
| 25. C2×C4⋊C8 | D3 | semidirect |
| 64. C2×C3×C4 | D8 | semidirect |
| 123. C2×C4 | D24 | semidirect |
| 147. C3 | #3245 | 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 |
| #4846 | 2 |
| #4843 | 2 |
| #3245 | 3 |