Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #26018359 | C2 | semidirect |
| 5. #26018354 | C2 | semidirect |
| 6. #26018353 | C2 | semidirect |
| 7. C89×#1386 | C2 | semidirect |
| 15. #19151633 | C4 | semidirect |
| 16. #106×D89 | C4 | semidirect |
| 155. #1386 | D89 | semidirect |
| 158. C89 | #12873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028843 | 2 |
| #26021872 | 2 |
| #26020295 | 2 |
| #26018359 | 2 |
| #26018354 | 2 |
| #26018353 | 2 |
| C89×#1386 | 2 |
| #12873 | 89 |