Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
650 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 111 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×#2275 | C2 | semidirect |
| 3. #71599 | C2 | semidirect |
| 4. #69492 | C2 | semidirect |
| 5. #69432 | C2 | semidirect |
| 6. #67621 | C2 | semidirect |
| 7. #67615 | C2 | semidirect |
| 19. #5015 | C4 | semidirect |
| 21. #5008 | C4 | semidirect |
| 31. #2275 | D3 | semidirect |
| 59. #874 | C2×C4 | semidirect |
| 62. #869 | C2×C4 | semidirect |
| 75. C4⋊(C3⋊C8) | C2×C4 | semidirect |
| 201. C3×D4 | #104 | semidirect |
| 324. D4 | #805 | semidirect |
| 385. C3 | #9325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2275 | 2 |
| #82310 | 2 |
| #71599 | 2 |
| #69492 | 2 |
| #69432 | 2 |
| #67621 | 2 |
| #67615 | 2 |
| #9325 | 3 |