Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
542 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 105 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. #74161 | C2 | semidirect |
| 5. C2×#4465 | C2 | semidirect |
| 6. #67659 | C2 | semidirect |
| 7. #67630 | C2 | semidirect |
| 20. #5071 | C4 | semidirect |
| 426. C3 | #9002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5071 | 2 |
| #74161 | 2 |
| C3×#1961 | 2 |
| #71765 | 2 |
| C2×#4465 | 2 |
| #67659 | 2 |
| #67630 | 2 |
| #9002 | 3 |