Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
328 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 117 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×#533 | C2 | semidirect |
| 3. #5089 | C2 | semidirect |
| 4. #5089 | C2 | semidirect |
| 5. #5081 | C2 | semidirect |
| 6. #5081 | C2 | semidirect |
| 7. #5066 | C2 | semidirect |
| 8. #5063 | C2 | semidirect |
| 10. #4996 | C2 | semidirect |
| 11. #4926 | C2 | semidirect |
| 44. #533 | D3 | semidirect |
| 245. C3 | #3240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#533 | 2 |
| #5479 | 2 |
| #5089 | 2 |
| #5081 | 2 |
| #5066 | 2 |
| #5063 | 2 |
| #5003 | 2 |
| #4996 | 2 |
| #4926 | 2 |
| #3240 | 3 |