Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26033354 | C2 | semidirect |
| 3. C2×#19151408 | C2 | semidirect |
| 4. #26020308 | C2 | semidirect |
| 5. #26018365 | C2 | semidirect |
| 6. #26018351 | C2 | semidirect |
| 7. C89×#2143 | C2 | semidirect |
| 14. #19151870 | C4 | semidirect |
| 15. #19151865 | C4 | semidirect |
| 182. #2143 | D89 | semidirect |
| 186. C89 | #13070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033354 | 2 |
| #26029968 | 2 |
| C2×#19151408 | 2 |
| #26020308 | 2 |
| #26018365 | 2 |
| #26018351 | 2 |
| C89×#2143 | 2 |
| #13070 | 89 |