Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2130 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2130 conjugacy classes of subgroups — too many to draw. Only its 667 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. #26028634 | C2 | semidirect |
| 2. #26028619 | C2 | semidirect |
| 3. #26028567 | C2 | semidirect |
| 4. C4×#15668006 | C2 | semidirect |
| 6. #26022735 | C2 | semidirect |
| 7. C2×C43×C89 | C2 | semidirect |
| 70. C42×C89 | #41 | semidirect |
| 79. C2×C4×C89 | #126 | semidirect |
| 112. C2×C43 | D89 | semidirect |
| 113. C89 | #36641 | semidirect |
| 176. C42 | #13083574 | semidirect |
| 192. C2×C4 | #15668006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028634 | 2 |
| #26028619 | 2 |
| #26028567 | 2 |
| C4×#15668006 | 2 |
| #26022742 | 2 |
| #26022735 | 2 |
| C2×C43×C89 | 2 |
| #36641 | 89 |