Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
486 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 4. C2×#19151375 | C2 | semidirect |
| 5. #26020139 | C2 | semidirect |
| 6. #26018359 | C2 | semidirect |
| 7. C89×#1383 | C2 | semidirect |
| 12. #19151709 | C4 | semidirect |
| 17. #19151410 | C4 | semidirect |
| 18. #19151400 | C4 | semidirect |
| 39. #15667952 | C2×C4 | semidirect |
| 41. #15667946 | C2×C4 | semidirect |
| 53. C2×C16×C89 | C2×C4 | semidirect |
| 55. #108×C89 | C2×C4 | semidirect |
| 152. #1383 | D89 | semidirect |
| 153. C89 | #12647 | semidirect |
| 192. C2×C16 | C4×D89 | semidirect |
| 194. #108 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151709 | 2 |
| C2×#19151410 | 2 |
| #26021969 | 2 |
| C2×#19151375 | 2 |
| #26020139 | 2 |
| #26018359 | 2 |
| C89×#1383 | 2 |
| #12647 | 89 |