Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 165 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. #26022509 | C2 | semidirect |
| 3. #26022294 | C2 | semidirect |
| 4. #26022292 | C2 | semidirect |
| 5. Q8×#13083549 | C2 | semidirect |
| 6. C4×#15667955 | C2 | semidirect |
| 7. C89×#3395 | C2 | semidirect |
| 58. #13083549 | #41 | semidirect |
| 76. Q8×C89 | SD32 | semidirect |
| 107. #3395 | D89 | semidirect |
| 114. C89 | #33959 | semidirect |
| 183. Q8 | #15667955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033227 | 2 |
| #26022509 | 2 |
| #26022294 | 2 |
| #26022292 | 2 |
| Q8×#13083549 | 2 |
| C4×#15667955 | 2 |
| C89×#3395 | 2 |
| #33959 | 89 |