Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 97 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. C2×#19152007 | C2 | semidirect |
| 4. #26021071 | C2 | semidirect |
| 5. C2×#19151339 | C2 | semidirect |
| 7. C89×#1295 | C2 | semidirect |
| 198. #1295 | D89 | semidirect |
| 199. C89 | #10086 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152007 | 2 |
| C2×#19151958 | 2 |
| #26028304 | 2 |
| #26021071 | 2 |
| C2×#19151339 | 2 |
| C2×#19151337 | 2 |
| C89×#1295 | 2 |
| #10086 | 89 |