Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
648 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #73471 | C2 | semidirect |
| 3. #69944 | C2 | semidirect |
| 4. C2×#4470 | C2 | semidirect |
| 5. #69456 | C2 | semidirect |
| 6. C3×#1282 | C2 | semidirect |
| 7. #67675 | C2 | semidirect |
| 24. #4736 | C4 | semidirect |
| 26. #4732 | C4 | semidirect |
| 38. #1282 | D3 | semidirect |
| 43. C22×D12 | C2×C4 | semidirect |
| 66. C2×C4⋊Dic3 | C2×C4 | semidirect |
| 76. C3×C22⋊C8 | C2×C4 | semidirect |
| 161. C3×C22⋊C4 | D8 | semidirect |
| 222. C22⋊C8 | C4×D3 | semidirect |
| 364. C22⋊C4 | D24 | semidirect |
| 527. C3 | #9277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #78611 | 2 |
| #73471 | 2 |
| #69944 | 2 |
| C2×#4470 | 2 |
| #69456 | 2 |
| C3×#1282 | 2 |
| #67675 | 2 |
| #9277 | 3 |