Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
574 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 103 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. C2×#5092 | C2 | semidirect |
| 4. C3×#1549 | C2 | semidirect |
| 5. #70524 | C2 | semidirect |
| 7. #67739 | C2 | semidirect |
| 34. #1549 | D3 | semidirect |
| 333. C3 | #10154 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5092 | 2 |
| #83199 | 2 |
| #79312 | 2 |
| C3×#1549 | 2 |
| #70524 | 2 |
| #70498 | 2 |
| #67739 | 2 |
| #10154 | 3 |