Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
528 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 1. #26031003 | C2 | semidirect |
| 2. #26022164 | C2 | semidirect |
| 3. #26018260 | C2 | semidirect |
| 4. #26018176 | C2 | semidirect |
| 5. C89×#1999 | C2 | semidirect |
| 13. C22⋊#13083549 | C22 | semidirect |
| 14. C22×D8×C89 | C22 | semidirect |
| 18. #340×C89 | C22 | semidirect |
| 22. C2×D712 | D4 | semidirect |
| 32. #15667946 | D4 | semidirect |
| 103. C23×C89 | D16 | semidirect |
| 174. #1999 | D89 | semidirect |
| 177. C89 | #12102 | semidirect |
| 178. C22×D8 | C2×D89 | semidirect |
| 190. #340 | C2×D89 | semidirect |
| 279. C23 | #15667953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031003 | 2 |
| #26022164 | 2 |
| #26018260 | 2 |
| #26018176 | 2 |
| C89×#1999 | 2 |
| #12102 | 89 |