Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
794 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 101 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. #83302 | C2 | semidirect |
| 2. #83297 | C2 | semidirect |
| 3. #73799 | C2 | semidirect |
| 4. C3×#1502 | C2 | semidirect |
| 5. #70774 | C2 | semidirect |
| 6. #70757 | C2 | semidirect |
| 7. #67620 | C2 | semidirect |
| 36. #1502 | D3 | semidirect |
| 46. C3×C4⋊Q8 | D4 | semidirect |
| 47. C3×#127 | D4 | semidirect |
| 85. C4⋊(C3⋊C8) | D4 | semidirect |
| 86. C4⋊(C3⋊C8) | D4 | semidirect |
| 148. C2×D12 | D8 | semidirect |
| 189. C4⋊Q8 | D12 | semidirect |
| 196. #127 | D12 | semidirect |
| 472. C3 | #10238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83302 | 2 |
| #83297 | 2 |
| #73799 | 2 |
| C3×#1502 | 2 |
| #70774 | 2 |
| #70757 | 2 |
| #67620 | 2 |
| #10238 | 3 |