Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
394 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 394 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 |
|---|---|---|
| 2. C2×#19151421 | C2 | semidirect |
| 5. #26021042 | C2 | semidirect |
| 6. #26018351 | C2 | semidirect |
| 7. C89×#1378 | C2 | semidirect |
| 21. #19151406 | C4 | semidirect |
| 45. #15667948 | C2×C4 | semidirect |
| 59. C2×C16×C89 | C2×C4 | semidirect |
| 158. #1378 | D89 | semidirect |
| 159. C89 | #12949 | semidirect |
| 202. C2×C16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029137 | 2 |
| C2×#19151421 | 2 |
| #26022002 | 2 |
| #26021981 | 2 |
| #26021042 | 2 |
| #26018351 | 2 |
| C89×#1378 | 2 |
| #12949 | 89 |