Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
512 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 2. #83324 | C2 | semidirect |
| 4. #71841 | C2 | semidirect |
| 6. #70456 | C2 | semidirect |
| 7. #67706 | C2 | semidirect |
| 372. C3 | #10202 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3246 | 2 |
| #83324 | 2 |
| #83283 | 2 |
| #71841 | 2 |
| #71811 | 2 |
| #70456 | 2 |
| #67706 | 2 |
| #10202 | 3 |