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. #26020554 | C2 | semidirect |
| 3. C4×#15667927 | C2 | semidirect |
| 4. #26018744 | C2 | semidirect |
| 5. C89×#1870 | C2 | semidirect |
| 6. #19152229 | C4 | semidirect |
| 10. #19152186 | C4 | semidirect |
| 11. #19152179 | C4 | semidirect |
| 200. C2×C4×C89 | #104 | semidirect |
| 268. #1870 | D89 | semidirect |
| 271. C89 | #8400 | semidirect |
| 488. C2×C4 | #15667938 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033674 | 2 |
| #26020554 | 2 |
| C4×#15667927 | 2 |
| #26018744 | 2 |
| C89×#1870 | 2 |
| #8400 | 89 |