Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
382 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 6. C2×#15668004 | C4 | semidirect |
| 7. #19151537 | C4 | semidirect |
| 9. #19151528 | C4 | semidirect |
| 16. #19151444 | C4 | semidirect |
| 166. C89 | #11846 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025950 | 2 |
| #26020329 | 2 |
| #26018277 | 2 |
| #26018253 | 2 |
| C89×#1458 | 2 |
| #11846 | 89 |