Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
478 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26021585 | C2 | semidirect |
| 2. #26021580 | C2 | semidirect |
| 4. #26018075 | C2 | semidirect |
| 5. #26018075 | C2 | semidirect |
| 109. C4⋊C4×C89 | SD16 | semidirect |
| 209. C89 | #7780 | semidirect |
| 311. C4⋊C4 | #13083562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021585 | 2 |
| #26021580 | 2 |
| #26021334 | 2 |
| #26018075 | 2 |
| #26018073 | 2 |
| C89×#2727 | 2 |
| #7780 | 89 |