Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
232 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 3. C3×#1368 | C2 | semidirect |
| 4. #67513 | C2 | semidirect |
| 5. #67464 | C2 | semidirect |
| 22. #1368 | D3 | semidirect |
| 67. C3×C16 | M16 | semidirect |
| 69. C3⋊C16 | M16 | semidirect |
| 120. C16 | ΓL(1,𝔽25) | semidirect |
| 155. C3 | #12020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #69071 | 2 |
| #68529 | 2 |
| C3×#1368 | 2 |
| #67513 | 2 |
| #67464 | 2 |
| #12020 | 3 |