Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
528 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 528 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 |
|---|---|---|
| 2. C2×#19151633 | C2 | semidirect |
| 3. C2×#19151408 | C2 | semidirect |
| 4. #26021862 | C2 | semidirect |
| 5. #26018359 | C2 | semidirect |
| 6. #26018358 | C2 | semidirect |
| 7. C2×#360×C89 | C2 | semidirect |
| 12. #19151836 | C4 | semidirect |
| 13. #19151831 | C4 | semidirect |
| 53. #15667944 | D4 | semidirect |
| 70. #106×C89 | D4 | semidirect |
| 193. C2×#360 | D89 | semidirect |
| 197. C89 | #13002 | semidirect |
| 258. #106 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029829 | 2 |
| C2×#19151633 | 2 |
| C2×#19151408 | 2 |
| #26021862 | 2 |
| #26018359 | 2 |
| #26018358 | 2 |
| C2×#360×C89 | 2 |
| #13002 | 89 |