Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
348 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26022450 | C2 | semidirect |
| 3. #26022430 | C2 | semidirect |
| 4. #26021677 | C2 | semidirect |
| 5. #26018263 | C2 | semidirect |
| 6. #26018175 | C2 | semidirect |
| 7. C89×#1347 | C2 | semidirect |
| 174. #1347 | D89 | semidirect |
| 176. C89 | #12280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031039 | 2 |
| #26022450 | 2 |
| #26022430 | 2 |
| #26021677 | 2 |
| #26018263 | 2 |
| #26018175 | 2 |
| C89×#1347 | 2 |
| #12280 | 89 |