Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
880 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 880 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. #26020172 | C2 | semidirect |
| 3. #26018590 | C2 | semidirect |
| 4. #26018157 | C2 | semidirect |
| 5. C89×#2973 | C2 | semidirect |
| 45. C2×M16×C89 | D4 | semidirect |
| 116. C23×C89 | #100 | semidirect |
| 198. #2973 | D89 | semidirect |
| 203. C89 | #9503 | semidirect |
| 232. C2×M16 | C22⋊D89 | semidirect |
| 327. C23 | #15667928 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023608 | 2 |
| #26020172 | 2 |
| #26018590 | 2 |
| #26018157 | 2 |
| C89×#2973 | 2 |
| #9503 | 89 |