Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26028840 | C2 | semidirect |
| 3. #26021989 | C2 | semidirect |
| 4. #26021987 | C2 | semidirect |
| 5. C2×#19151379 | C2 | semidirect |
| 6. #26018353 | C2 | semidirect |
| 7. C89×#1384 | C2 | semidirect |
| 13. #19151857 | C4 | semidirect |
| 14. #19151852 | C4 | semidirect |
| 33. C2×Dic356 | C2×C4 | semidirect |
| 35. C2×D712 | C2×C4 | semidirect |
| 60. #15667944 | D4 | semidirect |
| 72. #106×C89 | C2×C4 | semidirect |
| 73. #106×C89 | D4 | semidirect |
| 199. #1384 | D89 | semidirect |
| 200. C89 | #13008 | semidirect |
| 263. #106 | C4×D89 | semidirect |
| 264. #106 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029862 | 2 |
| #26028840 | 2 |
| #26021989 | 2 |
| #26021987 | 2 |
| C2×#19151379 | 2 |
| #26018353 | 2 |
| C89×#1384 | 2 |
| #13008 | 89 |