Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
786 conjugacy classes of subgroups; only the 283 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 283 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 |
|---|---|---|
| 3. #26020807 | C2 | semidirect |
| 4. #26020113 | C2 | semidirect |
| 6. C42×#10623494 | C2 | semidirect |
| 7. C89×#1839 | C2 | semidirect |
| 29. #15668006 | C8 | semidirect |
| 61. #13083553 | C2×C8 | semidirect |
| 76. C42×C89 | C2×C8 | semidirect |
| 101. #10623494 | #126 | semidirect |
| 123. #1839 | D89 | semidirect |
| 127. C89 | C8×#126 | semidirect |
| 196. C42 | C8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15668006 | 2 |
| #26020856 | 2 |
| #26020807 | 2 |
| #26020113 | 2 |
| #26020022 | 2 |
| C42×#10623494 | 2 |
| C89×#1839 | 2 |
| C8×#126 | 89 |