Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
226 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 69 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. #68525 | C2 | semidirect |
| 3. C3×#1368 | C2 | semidirect |
| 4. #67511 | C2 | semidirect |
| 5. #67465 | C2 | semidirect |
| 19. #1368 | D3 | semidirect |
| 58. C3×C16 | M16 | semidirect |
| 100. C16 | ΓL(1,𝔽25) | semidirect |
| 133. C3 | #12089 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #69078 | 2 |
| #68525 | 2 |
| C3×#1368 | 2 |
| #67511 | 2 |
| #67465 | 2 |
| #12089 | 3 |