Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
496 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26031405 | C2 | semidirect |
| 4. #26018934 | C2 | semidirect |
| 5. #26018654 | C2 | semidirect |
| 7. C89×#1301 | C2 | semidirect |
| 196. #1301 | D89 | semidirect |
| 197. C89 | #10190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031405 | 2 |
| #26030051 | 2 |
| C2×#19151879 | 2 |
| #26018934 | 2 |
| #26018654 | 2 |
| #26018572 | 2 |
| C89×#1301 | 2 |
| #10190 | 89 |