Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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. #26022033 | C2 | semidirect |
| 3. #26018453 | C2 | semidirect |
| 4. #26018452 | C2 | semidirect |
| 5. #26018430 | C2 | semidirect |
| 6. #26018389 | C2 | semidirect |
| 7. C89×#1415 | C2 | semidirect |
| 93. #1415 | D89 | semidirect |
| 95. C89 | #13713 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022335 | 2 |
| #26022033 | 2 |
| #26018453 | 2 |
| #26018452 | 2 |
| #26018430 | 2 |
| #26018389 | 2 |
| C89×#1415 | 2 |
| #13713 | 89 |