Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #5728 | C2 | semidirect |
| 3. C3×#461 | C2 | semidirect |
| 5. #5164 | C2 | semidirect |
| 6. #5090 | C2 | semidirect |
| 7. #5008 | C2 | semidirect |
| 8. #4850 | C2 | semidirect |
| 9. #4835 | C2 | semidirect |
| 10. #4814 | C2 | semidirect |
| 11. #4789 | C2 | semidirect |
| 50. #461 | D3 | semidirect |
| 267. C3 | #3116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| C4×#237 | 2 |
| C3×#461 | 2 |
| #5173 | 2 |
| #5164 | 2 |
| #5090 | 2 |
| #5008 | 2 |
| #4850 | 2 |
| #4835 | 2 |
| #4814 | 2 |
| #4789 | 2 |
| #3116 | 3 |