Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
224 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 55 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. #26022507 | C2 | semidirect |
| 2. #26022334 | C2 | semidirect |
| 4. #26022088 | C2 | semidirect |
| 5. #26018327 | C2 | semidirect |
| 6. #26018290 | C2 | semidirect |
| 7. C89×#1357 | C2 | semidirect |
| 114. #1357 | D89 | semidirect |
| 115. C89 | #12438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022507 | 2 |
| #26022334 | 2 |
| #26022325 | 2 |
| #26022088 | 2 |
| #26018327 | 2 |
| #26018290 | 2 |
| C89×#1357 | 2 |
| #12438 | 89 |