Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
648 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 648 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. #26018571 | C2 | semidirect |
| 4. #26018273 | C2 | semidirect |
| 5. #26018250 | C2 | semidirect |
| 6. #26018248 | C2 | semidirect |
| 7. C89×#1351 | C2 | semidirect |
| 8. C22×#13083575 | C4 | semidirect |
| 13. #19151517 | C4 | semidirect |
| 15. #19151516 | C4 | semidirect |
| 20. #19151445 | C4 | semidirect |
| 238. #1351 | D89 | semidirect |
| 241. C89 | #11725 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023469 | 2 |
| #26020039 | 2 |
| #26018571 | 2 |
| #26018273 | 2 |
| #26018250 | 2 |
| #26018248 | 2 |
| C89×#1351 | 2 |
| #11725 | 89 |