Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
452 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 17. C2×#15667946 | C4 | semidirect |
| 18. C2×#15667944 | C4 | semidirect |
| 20. C2×#15667937 | C4 | semidirect |
| 21. C2×#15667937 | C4 | semidirect |
| 221. C89 | #9240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151940 | 2 |
| #26028906 | 2 |
| #26020352 | 2 |
| #26018771 | 2 |
| #26018615 | 2 |
| #26018129 | 2 |
| C89×#1282 | 2 |
| #9240 | 89 |