Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
782 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26029291 | C2 | semidirect |
| 3. #26020196 | C2 | semidirect |
| 4. C4×#15667926 | C2 | semidirect |
| 5. #26018138 | C2 | semidirect |
| 6. #26018137 | C2 | semidirect |
| 7. C89×#1789 | C2 | semidirect |
| 17. #19151517 | C4 | semidirect |
| 19. #19151512 | C4 | semidirect |
| 20. #19151509 | C4 | semidirect |
| 22. #19151506 | C4 | semidirect |
| 34. C2×#13083558 | D4 | semidirect |
| 76. C2×M16×C89 | D4 | semidirect |
| 224. C2×Dic89 | #104 | semidirect |
| 279. #1789 | D89 | semidirect |
| 283. C89 | #9010 | semidirect |
| 322. C2×M16 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029291 | 2 |
| #26023465 | 2 |
| #26020196 | 2 |
| C4×#15667926 | 2 |
| #26018138 | 2 |
| #26018137 | 2 |
| C89×#1789 | 2 |
| #9010 | 89 |