Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26019985 | C2 | semidirect |
| 3. #26018253 | C2 | semidirect |
| 5. C89×#1458 | C2 | semidirect |
| 6. C2×C4×D356 | C4 | semidirect |
| 9. #19151528 | C4 | semidirect |
| 12. #19151515 | C4 | semidirect |
| 15. C4×C4⋊Dic89 | C4 | semidirect |
| 203. #1458 | D89 | semidirect |
| 206. C89 | #11691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023488 | 2 |
| #26019985 | 2 |
| #26018253 | 2 |
| #26018250 | 2 |
| C89×#1458 | 2 |
| #11691 | 89 |