Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
550 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 550 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. #83283 | C2 | semidirect |
| 3. #83271 | C2 | semidirect |
| 4. #71818 | C2 | semidirect |
| 5. #71811 | C2 | semidirect |
| 6. #70456 | C2 | semidirect |
| 7. #67706 | C2 | semidirect |
| 393. C3 | #10200 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3245 | 2 |
| #83283 | 2 |
| #83271 | 2 |
| #71818 | 2 |
| #71811 | 2 |
| #70456 | 2 |
| #67706 | 2 |
| #10200 | 3 |