Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1074 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 1. #26020716 | C2 | semidirect |
| 2. #26020550 | C2 | semidirect |
| 3. #26018612 | C2 | semidirect |
| 4. #26018590 | C2 | semidirect |
| 6. C22×#13083558 | C22 | semidirect |
| 8. #19151562 | C22 | semidirect |
| 10. C2×C22⋊#10623494 | C22 | semidirect |
| 161. C23×C89 | #100 | semidirect |
| 195. C2×C4×C89 | #100 | semidirect |
| 244. C89 | #8536 | semidirect |
| 400. C23 | #15667929 | semidirect |
| 434. C2×C4 | #15667929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020716 | 2 |
| #26020550 | 2 |
| #26018612 | 2 |
| #26018590 | 2 |
| C89×#3496 | 2 |
| #8536 | 89 |