Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
600 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26028671 | C2 | semidirect |
| 3. #26018694 | C2 | semidirect |
| 4. #26018118 | C2 | semidirect |
| 5. C89×#1464 | C2 | semidirect |
| 45. C4×#10623494 | D4 | semidirect |
| 193. #1464 | D89 | semidirect |
| 195. C89 | #9492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028671 | 2 |
| #26025818 | 2 |
| #26018694 | 2 |
| #26018118 | 2 |
| C89×#1464 | 2 |
| #9492 | 89 |