Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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×#1334 | C2 | semidirect |
| 5. #67764 | C2 | semidirect |
| 6. #67517 | C2 | semidirect |
| 7. #67466 | C2 | semidirect |
| 34. #1334 | D3 | semidirect |
| 290. C3 | #11681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79725 | 2 |
| #69071 | 2 |
| #68529 | 2 |
| C3×#1334 | 2 |
| #67764 | 2 |
| #67517 | 2 |
| #67466 | 2 |
| #11681 | 3 |