Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
390 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 103 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. #83331 | C2 | semidirect |
| 3. #71831 | C2 | semidirect |
| 6. #67756 | C2 | semidirect |
| 7. #67755 | C2 | semidirect |
| 313. C3 | #9372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3235 | 2 |
| #83331 | 2 |
| #71831 | 2 |
| #71800 | 2 |
| #71799 | 2 |
| #67756 | 2 |
| #67755 | 2 |
| #9372 | 3 |