Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
400 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 4. #70831 | C2 | semidirect |
| 5. C2×#4465 | C2 | semidirect |
| 6. #67751 | C2 | semidirect |
| 7. #67661 | C2 | semidirect |
| 380. C3 | #9266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83128 | 2 |
| #83121 | 2 |
| C3×#1532 | 2 |
| #70831 | 2 |
| C2×#4465 | 2 |
| #67751 | 2 |
| #67661 | 2 |
| #9266 | 3 |