Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
606 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 87 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. C4×#15667927 | C2 | semidirect |
| 3. #26018277 | C2 | semidirect |
| 4. #26018250 | C2 | semidirect |
| 5. C89×#1459 | C2 | semidirect |
| 6. C2×C4×D356 | C4 | semidirect |
| 10. #19151534 | C4 | semidirect |
| 13. #19151507 | C4 | semidirect |
| 17. #19151444 | C4 | semidirect |
| 208. #1459 | D89 | semidirect |
| 211. C89 | #11726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023531 | 2 |
| C4×#15667927 | 2 |
| #26018277 | 2 |
| #26018250 | 2 |
| C89×#1459 | 2 |
| #11726 | 89 |