Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
228 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 69 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. C3×#428 | C2 | semidirect |
| 3. C2×#822 | C2 | semidirect |
| 5. #4999 | C2 | semidirect |
| 7. #4530 | C2 | semidirect |
| 25. #428 | D3 | semidirect |
| 188. C3 | #2063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#428 | 2 |
| C2×#823 | 2 |
| C2×#822 | 2 |
| #5001 | 2 |
| #4999 | 2 |
| C2×#809 | 2 |
| #4530 | 2 |
| #2063 | 3 |