Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
584 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 584 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. #26030284 | C2 | semidirect |
| 3. #26030279 | C2 | semidirect |
| 4. #26021191 | C2 | semidirect |
| 5. #26018650 | C2 | semidirect |
| 6. #26018082 | C2 | semidirect |
| 7. C89×#1480 | C2 | semidirect |
| 106. C2×#10623494 | SD16 | semidirect |
| 214. #1480 | D89 | semidirect |
| 216. C89 | #10034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030697 | 2 |
| #26030284 | 2 |
| #26030279 | 2 |
| #26021191 | 2 |
| #26018650 | 2 |
| #26018082 | 2 |
| C89×#1480 | 2 |
| #10034 | 89 |