Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×C3×SD32 | C2 | semidirect |
| 2. #5192 | C2 | semidirect |
| 4. #4901 | C2 | semidirect |
| 5. #4565 | C2 | semidirect |
| 6. #4563 | C2 | semidirect |
| 7. #4506 | C2 | semidirect |
| 24. C2×SD32 | D3 | semidirect |
| 138. C3 | #2223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×SD32 | 2 |
| #5192 | 2 |
| #5160 | 2 |
| #4901 | 2 |
| #4565 | 2 |
| #4563 | 2 |
| #4506 | 2 |
| #2223 | 3 |