Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
584 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 584 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 |
|---|---|---|
| 2. #26030284 | C2 | semidirect |
| 3. #26021192 | C2 | semidirect |
| 4. #26018652 | C2 | semidirect |
| 5. C89×#1275 | C2 | semidirect |
| 84. C2×C8×C89 | SD16 | semidirect |
| 140. #1275 | D89 | semidirect |
| 141. C89 | #10034 | semidirect |
| 212. C2×C8 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030698 | 2 |
| #26030284 | 2 |
| #26021192 | 2 |
| #26018652 | 2 |
| C89×#1275 | 2 |
| #10034 | 89 |