Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
562 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×#5080 | C2 | semidirect |
| 4. C3×#1997 | C2 | semidirect |
| 5. #70506 | C2 | semidirect |
| 7. #67667 | C2 | semidirect |
| 33. #1997 | D3 | semidirect |
| 339. C3 | #10172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83216 | 2 |
| C2×#5080 | 2 |
| #78538 | 2 |
| C3×#1997 | 2 |
| #70506 | 2 |
| #70498 | 2 |
| #67667 | 2 |
| #10172 | 3 |