Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
912 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 111 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. #83355 | C2 | semidirect |
| 3. C3×#1994 | C2 | semidirect |
| 4. #70502 | C2 | semidirect |
| 5. #67611 | C2 | semidirect |
| 22. #1994 | D3 | semidirect |
| 30. C3×C4⋊Q8 | D4 | semidirect |
| 49. C4⋊(C3⋊C8) | D4 | semidirect |
| 90. C3×C42 | SD16 | semidirect |
| 102. C4⋊Q8 | D12 | semidirect |
| 176. C42 | #215 | semidirect |
| 238. C3 | #10290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83355 | 2 |
| #73318 | 2 |
| C3×#1994 | 2 |
| #70502 | 2 |
| #67611 | 2 |
| #10290 | 3 |