Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
632 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 632 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. #73389 | C2 | semidirect |
| 3. #70790 | C2 | semidirect |
| 4. #70774 | C2 | semidirect |
| 5. #69440 | C2 | semidirect |
| 6. C3×#1274 | C2 | semidirect |
| 7. #67738 | C2 | semidirect |
| 22. #4695 | C4 | semidirect |
| 23. #4694 | C4 | semidirect |
| 34. #1274 | D3 | semidirect |
| 55. #874 | C2×C4 | semidirect |
| 61. #869 | C2×C4 | semidirect |
| 67. C3×C4×C8 | C2×C4 | semidirect |
| 133. C3×C42 | D8 | semidirect |
| 188. C4×C8 | C4×D3 | semidirect |
| 296. C42 | D24 | semidirect |
| 415. C3 | #9299 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79303 | 2 |
| #73389 | 2 |
| #70790 | 2 |
| #70774 | 2 |
| #69440 | 2 |
| C3×#1274 | 2 |
| #67738 | 2 |
| #9299 | 3 |