Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
518 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26030801 | C2 | semidirect |
| 4. #26018804 | C2 | semidirect |
| 6. #26018118 | C2 | semidirect |
| 7. C89×#1534 | C2 | semidirect |
| 198. #1534 | D89 | semidirect |
| 202. C89 | #10023 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030801 | 2 |
| #26030352 | 2 |
| #26026121 | 2 |
| #26018804 | 2 |
| #26018694 | 2 |
| #26018118 | 2 |
| C89×#1534 | 2 |
| #10023 | 89 |