Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
706 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 706 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. #79288 | C2 | semidirect |
| 3. C3×#1545 | C2 | semidirect |
| 4. #71759 | C2 | semidirect |
| 5. #70527 | C2 | semidirect |
| 6. #67746 | C2 | semidirect |
| 7. #67715 | C2 | semidirect |
| 31. #1545 | D3 | semidirect |
| 62. C3×C4⋊C8 | D4 | semidirect |
| 71. C4⋊(C3⋊C8) | D4 | semidirect |
| 174. C4⋊C8 | #67 | semidirect |
| 385. C3 | #9405 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83188 | 2 |
| #79288 | 2 |
| C3×#1545 | 2 |
| #71759 | 2 |
| #70527 | 2 |
| #67746 | 2 |
| #67715 | 2 |
| #9405 | 3 |