Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26028523 | C2 | semidirect |
| 5. #26018281 | C2 | semidirect |
| 6. #26018195 | C2 | semidirect |
| 7. C89×#1354 | C2 | semidirect |
| 92. C4×Dic89 | SD16 | semidirect |
| 182. #1354 | D89 | semidirect |
| 184. C89 | #12184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028523 | 2 |
| #26021482 | 2 |
| #26019223 | 2 |
| #26019220 | 2 |
| #26018281 | 2 |
| #26018195 | 2 |
| C89×#1354 | 2 |
| #12184 | 89 |