Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
348 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 57 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. #26021922 | C2 | semidirect |
| 3. #26021918 | C2 | semidirect |
| 4. #26018423 | C2 | semidirect |
| 5. #26018414 | C2 | semidirect |
| 6. #26018414 | C2 | semidirect |
| 7. C89×#1412 | C2 | semidirect |
| 8. #19152204 | C4 | semidirect |
| 10. #19151987 | C4 | semidirect |
| 12. #19151955 | C4 | semidirect |
| 17. #19151660 | C4 | semidirect |
| 33. #15668009 | C2×C4 | semidirect |
| 54. C4×#10623494 | C2×C4 | semidirect |
| 56. #125×C89 | C2×C4 | semidirect |
| 61. #97×C89 | C2×C4 | semidirect |
| 176. #1412 | D89 | semidirect |
| 179. C89 | #13609 | semidirect |
| 208. #125 | C4×D89 | semidirect |
| 232. #97 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031303 | 2 |
| #26021922 | 2 |
| #26021918 | 2 |
| #26018423 | 2 |
| #26018414 | 2 |
| C89×#1412 | 2 |
| #13609 | 89 |