Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
306 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 21. #4480 | C4 | semidirect |
| 22. #4479 | C4 | semidirect |
| 241. C3 | #9629 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #70750 | 2 |
| #70745 | 2 |
| #70516 | 2 |
| #70493 | 2 |
| C4⋊C4×C3⋊C8 | 2 |
| C3×#1303 | 2 |
| #67620 | 2 |
| #9629 | 3 |