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. #26031251 | C2 | semidirect |
| 3. #26018966 | C2 | semidirect |
| 4. #26018849 | C2 | semidirect |
| 5. #26018764 | C2 | semidirect |
| 6. #26018146 | C2 | semidirect |
| 7. C89×#3138 | C2 | semidirect |
| 47. C4⋊#10623494 | D4 | semidirect |
| 60. C4⋊Q8×C89 | D4 | semidirect |
| 61. C4⋊Q8×C89 | D4 | semidirect |
| 75. #97×C89 | D4 | semidirect |
| 202. #3138 | D89 | semidirect |
| 208. C89 | #10096 | semidirect |
| 241. C4⋊Q8 | C22⋊D89 | semidirect |
| 242. C4⋊Q8 | C22⋊D89 | semidirect |
| 274. #97 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031251 | 2 |
| #26026359 | 2 |
| #26018966 | 2 |
| #26018849 | 2 |
| #26018764 | 2 |
| #26018146 | 2 |
| C89×#3138 | 2 |
| #10096 | 89 |