Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
390 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. C3×#1350 | C2 | semidirect |
| 5. #67777 | C2 | semidirect |
| 6. #67529 | C2 | semidirect |
| 7. #67488 | C2 | semidirect |
| 34. #1350 | D3 | semidirect |
| 342. C3 | #11896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#467 | 2 |
| #69106 | 2 |
| #68939 | 2 |
| C3×#1350 | 2 |
| #67777 | 2 |
| #67529 | 2 |
| #67488 | 2 |
| #11896 | 3 |