Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
774 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26023093 | C2 | semidirect |
| 3. #26021088 | C2 | semidirect |
| 4. #26018769 | C2 | semidirect |
| 5. #26018159 | C2 | semidirect |
| 6. #26018138 | C2 | semidirect |
| 7. C89×#1789 | C2 | semidirect |
| 8. C2×#15668037 | C4 | semidirect |
| 14. #19151599 | C4 | semidirect |
| 155. Q8×C89 | #99 | semidirect |
| 241. #1789 | D89 | semidirect |
| 245. C89 | #9368 | semidirect |
| 393. Q8 | #15667926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029504 | 2 |
| #26023093 | 2 |
| #26021088 | 2 |
| #26018769 | 2 |
| #26018159 | 2 |
| #26018138 | 2 |
| C89×#1789 | 2 |
| #9368 | 89 |