Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
650 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26031167 | C2 | semidirect |
| 2. #26021076 | C2 | semidirect |
| 3. #26018812 | C2 | semidirect |
| 4. #26018097 | C2 | semidirect |
| 5. C89×#3150 | C2 | semidirect |
| 76. C2×C8×C89 | D8 | semidirect |
| 138. #3150 | D89 | semidirect |
| 142. C89 | #10218 | semidirect |
| 212. C2×C8 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031167 | 2 |
| #26021076 | 2 |
| #26018812 | 2 |
| #26018097 | 2 |
| C89×#3150 | 2 |
| #10218 | 89 |