Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
564 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26031190 | C2 | semidirect |
| 3. #26021076 | C2 | semidirect |
| 4. #26018816 | C2 | semidirect |
| 5. #26018812 | C2 | semidirect |
| 6. #26018097 | C2 | semidirect |
| 7. C89×#3135 | C2 | semidirect |
| 199. #3135 | D89 | semidirect |
| 204. C89 | #10219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031190 | 2 |
| #26031167 | 2 |
| #26021076 | 2 |
| #26018816 | 2 |
| #26018812 | 2 |
| #26018097 | 2 |
| C89×#3135 | 2 |
| #10219 | 89 |