Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 139 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. #26021241 | C2 | semidirect |
| 4. #26019008 | C2 | semidirect |
| 5. #26018932 | C2 | semidirect |
| 7. C8×M16×C89 | C2 | semidirect |
| 90. M16×C89 | SD16 | semidirect |
| 129. C8×C89 | #100 | semidirect |
| 160. C8×M16 | D89 | semidirect |
| 161. C89 | #9793 | semidirect |
| 238. M16 | #13083563 | semidirect |
| 285. C8 | #15667928 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151971 | 2 |
| #26021241 | 2 |
| #26021092 | 2 |
| #26019008 | 2 |
| #26018932 | 2 |
| #26018919 | 2 |
| C8×M16×C89 | 2 |
| #9793 | 89 |