Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
858 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 858 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #26020552 | C2 | semidirect |
| 3. #26020550 | C2 | semidirect |
| 4. #26018741 | C2 | semidirect |
| 5. C4×#99×C89 | C2 | semidirect |
| 7. #19152229 | C4 | semidirect |
| 11. #19152186 | C4 | semidirect |
| 12. #19152179 | C4 | semidirect |
| 203. C2×C4×C89 | #104 | semidirect |
| 269. C4×#99 | D89 | semidirect |
| 271. C89 | #8400 | semidirect |
| 488. C2×C4 | #15667940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033674 | 2 |
| #26020552 | 2 |
| #26020550 | 2 |
| #26018741 | 2 |
| C4×#99×C89 | 2 |
| #8400 | 89 |