Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
440 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26018576 | C2 | semidirect |
| 2. #26018198 | C2 | semidirect |
| 24. #124×C89 | C8 | semidirect |
| 137. C89 | #11480 | semidirect |
| 154. #124 | #10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018576 | 2 |
| #26018198 | 2 |
| #26018184 | 2 |
| C89×#2326 | 2 |
| #11480 | 89 |