Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
306 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 83 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. #69065 | C2 | semidirect |
| 2. #69061 | C2 | semidirect |
| 4. #69058 | C2 | semidirect |
| 5. #68060 | C2 | semidirect |
| 6. #68058 | C2 | semidirect |
| 7. C3×#1312 | C2 | semidirect |
| 30. #1312 | D3 | semidirect |
| 219. C3 | #12527 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #69065 | 2 |
| #69061 | 2 |
| #69060 | 2 |
| #69058 | 2 |
| #68060 | 2 |
| #68058 | 2 |
| C3×#1312 | 2 |
| #12527 | 3 |