Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
880 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26029281 | C2 | semidirect |
| 2. #26020173 | C2 | semidirect |
| 3. #26018590 | C2 | semidirect |
| 4. #26018158 | C2 | semidirect |
| 24. C2×#13083558 | D4 | semidirect |
| 129. C23×C89 | #100 | semidirect |
| 203. C89 | #9503 | semidirect |
| 327. C23 | #15667929 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029281 | 2 |
| #26020173 | 2 |
| #26018590 | 2 |
| #26018158 | 2 |
| C89×#2408 | 2 |
| #9503 | 89 |