Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
500 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 83 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. #26018277 | C2 | semidirect |
| 5. C89×#1464 | C2 | semidirect |
| 6. C2×C4×D356 | C4 | semidirect |
| 8. #19151537 | C4 | semidirect |
| 10. #19151515 | C4 | semidirect |
| 16. #19151466 | C4 | semidirect |
| 197. #1464 | D89 | semidirect |
| 200. C89 | #11754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025818 | 2 |
| #26019985 | 2 |
| #26018277 | 2 |
| #26018250 | 2 |
| C89×#1464 | 2 |
| #11754 | 89 |