Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
522 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26029052 | C2 | semidirect |
| 3. C2×#19151409 | C2 | semidirect |
| 4. #26021129 | C2 | semidirect |
| 5. #26018357 | C2 | semidirect |
| 6. #26018335 | C2 | semidirect |
| 7. C89×#2140 | C2 | semidirect |
| 11. #19152034 | C4 | semidirect |
| 48. #15667952 | C2×C4 | semidirect |
| 63. C2×D8×C89 | C2×C4 | semidirect |
| 83. Dic356 | C22⋊C4 | semidirect |
| 87. D712 | C22⋊C4 | semidirect |
| 188. #2140 | D89 | semidirect |
| 192. C89 | #13025 | semidirect |
| 227. C2×D8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152034 | 2 |
| #26029052 | 2 |
| C2×#19151409 | 2 |
| #26021129 | 2 |
| #26018357 | 2 |
| #26018335 | 2 |
| C89×#2140 | 2 |
| #13025 | 89 |