Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 4. #26021035 | C2 | semidirect |
| 5. #26018360 | C2 | semidirect |
| 6. #26018340 | C2 | semidirect |
| 7. C2×#367×C89 | C2 | semidirect |
| 18. #19151406 | C4 | semidirect |
| 46. #15667948 | C2×C4 | semidirect |
| 58. C2×C16×C89 | C2×C4 | semidirect |
| 161. C2×#367 | D89 | semidirect |
| 167. C89 | #12946 | semidirect |
| 210. C2×C16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029126 | 2 |
| C2×#19151406 | 2 |
| #26021962 | 2 |
| #26021035 | 2 |
| #26018360 | 2 |
| #26018340 | 2 |
| C2×#367×C89 | 2 |
| #12946 | 89 |