Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
576 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26030347 | C2 | semidirect |
| 3. #26018876 | C2 | semidirect |
| 4. #26018803 | C2 | semidirect |
| 5. #26018696 | C2 | semidirect |
| 6. #26018117 | C2 | semidirect |
| 7. C89×#3140 | C2 | semidirect |
| 53. #15667923 | D4 | semidirect |
| 61. C4⋊Q8×C89 | D4 | semidirect |
| 62. C4⋊Q8×C89 | D4 | semidirect |
| 81. C4×C8×C89 | D4 | semidirect |
| 211. #3140 | D89 | semidirect |
| 218. C89 | #10022 | semidirect |
| 251. C4⋊Q8 | C22⋊D89 | semidirect |
| 252. C4⋊Q8 | C22⋊D89 | semidirect |
| 288. C4×C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030347 | 2 |
| #26026105 | 2 |
| #26018876 | 2 |
| #26018803 | 2 |
| #26018696 | 2 |
| #26018117 | 2 |
| C89×#3140 | 2 |
| #10022 | 89 |