Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
770 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 770 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. #26021099 | C2 | semidirect |
| 3. #26018972 | C2 | semidirect |
| 4. #26018859 | C2 | semidirect |
| 5. #26018668 | C2 | semidirect |
| 6. #26018603 | C2 | semidirect |
| 7. C89×#1495 | C2 | semidirect |
| 22. #19151655 | C22 | semidirect |
| 25. C4×#13083558 | C22 | semidirect |
| 33. #431×C89 | C22 | semidirect |
| 34. #423×C89 | C22 | semidirect |
| 281. #1495 | D89 | semidirect |
| 284. C89 | #8483 | semidirect |
| 301. #431 | C2×D89 | semidirect |
| 302. #423 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034768 | 2 |
| #26021099 | 2 |
| #26018972 | 2 |
| #26018859 | 2 |
| #26018668 | 2 |
| #26018603 | 2 |
| C89×#1495 | 2 |
| #8483 | 89 |