Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #26021973 | C2 | semidirect |
| 4. #26021971 | C2 | semidirect |
| 6. #26018359 | C2 | semidirect |
| 7. C89×#1386 | C2 | semidirect |
| 14. #19151857 | C4 | semidirect |
| 33. C2×Dic356 | C2×C4 | semidirect |
| 69. #106×C89 | C2×C4 | semidirect |
| 184. #1386 | D89 | semidirect |
| 185. C89 | #13000 | semidirect |
| 246. #106 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151857 | 2 |
| #26028840 | 2 |
| #26021973 | 2 |
| #26021971 | 2 |
| C2×#19151379 | 2 |
| #26018359 | 2 |
| C89×#1386 | 2 |
| #13000 | 89 |