Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
4038 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 4038 conjugacy classes of subgroups — too many to draw. Only its 827 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. C22×C3×#127 | C2 | semidirect |
| 2. C23×#214 | C2 | semidirect |
| 3. C23×#213 | C2 | semidirect |
| 4. C22×#875 | C2 | semidirect |
| 5. C2×#5074 | C2 | direct (N × H) |
| 6. C22×#803 | C2 | semidirect |
| 13. C2×C3×#127 | C22 | semidirect |
| 16. C22×#214 | C22 | semidirect |
| 18. C22×#213 | C22 | semidirect |
| 22. C2×#875 | C22 | semidirect |
| 23. #5074 | C22 | direct (N × H) |
| 24. C2×#803 | C22 | semidirect |
| 27. C22×#127 | D3 | semidirect |
| 49. C3×#127 | C23 | semidirect |
| 53. C2×#214 | C23 | semidirect |
| 55. C2×#213 | C23 | semidirect |
| 57. C22×C3⋊C8 | D4 | semidirect |
| 60. #875 | C23 | semidirect |
| 61. #803 | C23 | semidirect |
| 72. C2×#127 | C2×D3 | semidirect |
| 113. C2×C3⋊C8 | C2×D4 | semidirect |
| 139. #127 | C22×D3 | semidirect |
| 173. C3⋊C8 | C22×D4 | semidirect |
| 213. C22×C3 | #496 | semidirect |
| 253. C2×C3 | C2×#496 | semidirect |
| 263. C22 | #5074 | direct (N × H) |
| 271. C3 | C22×#496 | semidirect |
| 274. C2 | C2×#5074 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#127 | 2 |
| C23×#214 | 2 |
| C23×#213 | 2 |
| C22×#875 | 2 |
| C2×#5074 | 2 |
| C22×#803 | 2 |
| C22×#496 | 3 |