Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 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. C3×#536 | C2 | semidirect |
| 3. C2×#942 | C2 | semidirect |
| 4. #5523 | C2 | semidirect |
| 5. #5232 | C2 | semidirect |
| 6. C2×#835 | C2 | semidirect |
| 7. #5090 | C2 | semidirect |
| 8. #5083 | C2 | semidirect |
| 9. #5057 | C2 | semidirect |
| 10. #5054 | C2 | semidirect |
| 11. #4999 | C2 | semidirect |
| 46. #536 | D3 | semidirect |
| 286. C3 | #3046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#536 | 2 |
| C2×#950 | 2 |
| C2×#942 | 2 |
| #5523 | 2 |
| #5232 | 2 |
| C2×#835 | 2 |
| #5090 | 2 |
| #5083 | 2 |
| #5057 | 2 |
| #5054 | 2 |
| #4999 | 2 |
| #3046 | 3 |