Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
704 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26028698 | C2 | semidirect |
| 3. #26020193 | C2 | semidirect |
| 4. #26018821 | C2 | semidirect |
| 5. #26018611 | C2 | semidirect |
| 6. #26018157 | C2 | semidirect |
| 7. C89×#1298 | C2 | semidirect |
| 9. C2×#15668040 | C4 | semidirect |
| 10. C2×#15668040 | C4 | semidirect |
| 17. #19151600 | C4 | semidirect |
| 18. #19151600 | C4 | semidirect |
| 287. #1298 | D89 | semidirect |
| 288. C89 | #9347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029506 | 2 |
| #26028698 | 2 |
| #26020193 | 2 |
| #26018821 | 2 |
| #26018611 | 2 |
| #26018157 | 2 |
| C89×#1298 | 2 |
| #9347 | 89 |