Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
532 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26021237 | C2 | semidirect |
| 5. #26020675 | C2 | semidirect |
| 6. #26018120 | C2 | semidirect |
| 7. C89×#1850 | C2 | semidirect |
| 144. C22⋊C4×C89 | SD16 | semidirect |
| 256. #1850 | D89 | semidirect |
| 258. C89 | #10565 | semidirect |
| 395. C22⋊C4 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031010 | 2 |
| #26021237 | 2 |
| #26021088 | 2 |
| #26020680 | 2 |
| #26020675 | 2 |
| #26018120 | 2 |
| C89×#1850 | 2 |
| #10565 | 89 |