Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
606 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26020039 | C2 | semidirect |
| 3. #26018567 | C2 | semidirect |
| 4. #26018276 | C2 | semidirect |
| 5. #26018250 | C2 | semidirect |
| 6. #26018248 | C2 | semidirect |
| 7. C89×#1352 | C2 | semidirect |
| 9. C2×#15667974 | C4 | semidirect |
| 15. #19151533 | C4 | semidirect |
| 16. #19151508 | C4 | semidirect |
| 20. #19151443 | C4 | semidirect |
| 233. #1352 | D89 | semidirect |
| 236. C89 | #11726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023532 | 2 |
| #26020039 | 2 |
| #26018567 | 2 |
| #26018276 | 2 |
| #26018250 | 2 |
| #26018248 | 2 |
| C89×#1352 | 2 |
| #11726 | 89 |