Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
570 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 570 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26031382 | C2 | semidirect |
| 2. #26031179 | C2 | semidirect |
| 4. #26021225 | C2 | semidirect |
| 5. #26018813 | C2 | semidirect |
| 6. #26018813 | C2 | semidirect |
| 7. C89×#1281 | C2 | semidirect |
| 123. C2×C8×C89 | SD16 | semidirect |
| 202. #1281 | D89 | semidirect |
| 203. C89 | #10221 | semidirect |
| 306. C2×C8 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031382 | 2 |
| #26031179 | 2 |
| #26030698 | 2 |
| #26021225 | 2 |
| #26018813 | 2 |
| C89×#1281 | 2 |
| #10221 | 89 |