Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
794 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 119 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. #26020718 | C2 | semidirect |
| 4. #26018617 | C2 | semidirect |
| 144. C23×C89 | #101 | semidirect |
| 163. C2×C4×C89 | #101 | semidirect |
| 218. C89 | #8537 | semidirect |
| 357. C23 | #15667930 | semidirect |
| 387. C2×C4 | #15667930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034055 | 2 |
| #26020718 | 2 |
| #26020550 | 2 |
| #26018617 | 2 |
| C89×#1465 | 2 |
| #8537 | 89 |