Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
250 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#4449 | C2 | semidirect |
| 2. #69066 | C2 | semidirect |
| 4. C3×C4×C32 | C2 | semidirect |
| 18. C4×C32 | D3 | semidirect |
| 32. C3×C32 | D4 | semidirect |
| 70. C32 | D12 | semidirect |
| 101. C3×C4 | SD64 | semidirect |
| 124. C4 | #4449 | semidirect |
| 127. C3 | #13727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4449 | 2 |
| #69066 | 2 |
| #69060 | 2 |
| C3×C4×C32 | 2 |
| #13727 | 3 |