Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
212 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 212 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 |
|---|---|---|
| 2. #70923 | C2 | semidirect |
| 3. #67766 | C2 | semidirect |
| 4. #67502 | C2 | semidirect |
| 5. #67498 | C2 | semidirect |
| 24. C3×Q32 | C8 | semidirect |
| 25. C3×SD32 | C8 | semidirect |
| 26. C3×D16 | C8 | semidirect |
| 67. Q32 | C3⋊C8 | semidirect |
| 68. SD32 | C3⋊C8 | semidirect |
| 69. D16 | C3⋊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 |
|---|---|
| C3×#2178 | 2 |
| #70923 | 2 |
| #67766 | 2 |
| #67502 | 2 |
| #67498 | 2 |
| #12047 | 3 |