Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
504 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26021861 | C2 | semidirect |
| 3. #340×D89 | C2 | semidirect |
| 4. #26018264 | C2 | semidirect |
| 5. #26018262 | C2 | semidirect |
| 6. #26018260 | C2 | semidirect |
| 7. C89×#1348 | C2 | semidirect |
| 8. C2×#15668035 | C4 | semidirect |
| 13. #19151836 | C4 | semidirect |
| 14. #19151835 | C4 | semidirect |
| 18. #19151635 | C4 | semidirect |
| 32. C2×D712 | C2×C4 | semidirect |
| 53. #15667946 | C2×C4 | semidirect |
| 58. C2×Q16×C89 | C2×C4 | semidirect |
| 63. #107×C89 | C2×C4 | semidirect |
| 200. #1348 | D89 | semidirect |
| 203. C89 | #11704 | semidirect |
| 227. C2×Q16 | C4×D89 | semidirect |
| 255. #107 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029835 | 2 |
| #26021861 | 2 |
| #340×D89 | 2 |
| #26018264 | 2 |
| #26018262 | 2 |
| #26018260 | 2 |
| C89×#1348 | 2 |
| #11704 | 89 |