Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
628 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26029279 | C2 | semidirect |
| 3. #26018588 | C2 | semidirect |
| 4. #26018578 | C2 | semidirect |
| 5. #26018578 | C2 | semidirect |
| 6. #26018158 | C2 | semidirect |
| 7. C89×#1305 | C2 | semidirect |
| 64. C22⋊#10623494 | D4 | semidirect |
| 78. C22⋊C8×C89 | D4 | semidirect |
| 266. #1305 | D89 | semidirect |
| 267. C89 | #9515 | semidirect |
| 335. C22⋊C8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029279 | 2 |
| #26025144 | 2 |
| #26018588 | 2 |
| #26018578 | 2 |
| #26018158 | 2 |
| C89×#1305 | 2 |
| #9515 | 89 |