Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
546 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 99 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. #79312 | C2 | semidirect |
| 4. C3×#1502 | C2 | semidirect |
| 5. #69492 | C2 | semidirect |
| 6. #69489 | C2 | semidirect |
| 7. #67744 | C2 | semidirect |
| 37. #1502 | D3 | semidirect |
| 389. C3 | #10196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83310 | 2 |
| #83283 | 2 |
| #79312 | 2 |
| C3×#1502 | 2 |
| #69492 | 2 |
| #69489 | 2 |
| #67744 | 2 |
| #10196 | 3 |