Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
212 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. #69300 | C2 | semidirect |
| 3. C3×#1373 | C2 | semidirect |
| 4. #67568 | C2 | semidirect |
| 5. #67498 | C2 | semidirect |
| 19. #1373 | D3 | semidirect |
| 33. Dic24 | C8 | semidirect |
| 34. #800 | C8 | semidirect |
| 35. D48 | C8 | semidirect |
| 137. C3 | #12047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #69300 | 2 |
| #69067 | 2 |
| C3×#1373 | 2 |
| #67568 | 2 |
| #67498 | 2 |
| #12047 | 3 |