Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
470 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 95 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. #26021195 | C2 | semidirect |
| 5. #26019005 | C2 | semidirect |
| 6. #26018943 | C2 | semidirect |
| 7. C89×#1303 | C2 | semidirect |
| 90. #13083558 | SD16 | semidirect |
| 197. #1303 | D89 | semidirect |
| 198. C89 | #10504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031195 | 2 |
| #26021195 | 2 |
| #26021179 | 2 |
| #26021091 | 2 |
| #26019005 | 2 |
| #26018943 | 2 |
| C89×#1303 | 2 |
| #10504 | 89 |