Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
684 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. #26031257 | C2 | semidirect |
| 2. #26030627 | C2 | semidirect |
| 4. #26018965 | C2 | semidirect |
| 5. #26018849 | C2 | semidirect |
| 6. #26018763 | C2 | semidirect |
| 7. C89×#1300 | C2 | semidirect |
| 39. #15668012 | D4 | semidirect |
| 40. #15668012 | D4 | semidirect |
| 70. C4⋊C8×C89 | D4 | semidirect |
| 73. #97×C89 | D4 | semidirect |
| 207. #1300 | D89 | semidirect |
| 208. C89 | #10096 | semidirect |
| 265. C4⋊C8 | D356 | semidirect |
| 274. #97 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031257 | 2 |
| #26030627 | 2 |
| #26026358 | 2 |
| #26018965 | 2 |
| #26018849 | 2 |
| #26018763 | 2 |
| C89×#1300 | 2 |
| #10096 | 89 |