Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
224 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26022330 | C2 | semidirect |
| 3. #26022090 | C2 | semidirect |
| 4. #26018328 | C2 | semidirect |
| 5. #26018291 | C2 | semidirect |
| 6. #26018289 | C2 | semidirect |
| 7. C89×#2248 | C2 | semidirect |
| 108. #2248 | 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 |
|---|---|
| #26022330 | 2 |
| #26022325 | 2 |
| #26022090 | 2 |
| #26018328 | 2 |
| #26018291 | 2 |
| #26018289 | 2 |
| C89×#2248 | 2 |
| #12438 | 89 |