Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
602 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19151393 | C2 | semidirect |
| 3. #26020240 | C2 | semidirect |
| 4. C4×#15667927 | C2 | semidirect |
| 15. C2×#124×C89 | C4 | semidirect |
| 20. #391×C89 | C4 | semidirect |
| 21. #390×C89 | C4 | semidirect |
| 24. C4×C4⋊C4×C89 | C4 | semidirect |
| 231. C89 | #13225 | semidirect |
| 233. C2×#124 | Dic89 | semidirect |
| 240. #391 | Dic89 | semidirect |
| 241. #390 | Dic89 | semidirect |
| 245. C4×C4⋊C4 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151393 | 2 |
| C2×#19151391 | 2 |
| #26020240 | 2 |
| C4×#15667927 | 2 |
| C89×#2544 | 2 |
| #13225 | 89 |