Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
768 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 87 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. C4×#15667929 | C2 | semidirect |
| 3. #26018256 | C2 | semidirect |
| 4. C89×#1465 | C2 | semidirect |
| 15. #19151367 | C22 | semidirect |
| 18. #324×C89 | C22 | semidirect |
| 192. #1465 | D89 | semidirect |
| 194. C89 | #11779 | semidirect |
| 208. #324 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023608 | 2 |
| C4×#15667929 | 2 |
| #26018256 | 2 |
| C89×#1465 | 2 |
| #11779 | 89 |