Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
508 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 508 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. C2×#19151719 | C2 | semidirect |
| 3. C2×#19151410 | C2 | semidirect |
| 4. C2×#19151407 | C2 | semidirect |
| 5. #26021126 | C2 | semidirect |
| 6. #26018331 | C2 | semidirect |
| 7. C89×#1383 | C2 | semidirect |
| 13. C2×#15667957 | C4 | semidirect |
| 14. C2×D1424 | C4 | semidirect |
| 85. Dic356 | C22⋊C4 | semidirect |
| 93. D712 | C22⋊C4 | semidirect |
| 183. #1383 | D89 | semidirect |
| 185. C89 | #13040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152036 | 2 |
| C2×#19151719 | 2 |
| C2×#19151410 | 2 |
| C2×#19151407 | 2 |
| #26021126 | 2 |
| #26018331 | 2 |
| C89×#1383 | 2 |
| #13040 | 89 |