Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1502 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1502 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
|---|---|---|
| 3. C2×#19151392 | C2 | direct (N × H) |
| 5. C23×Dic178 | C4 | semidirect |
| 8. C2×#15667999 | C4 | semidirect |
| 13. C22×C4×Dic89 | C4 | semidirect |
| 16. #19151392 | C22 | direct (N × H) |
| 24. C22×Dic178 | C2×C4 | semidirect |
| 31. #15667999 | C2×C4 | semidirect |
| 40. C2×C4×Dic89 | C2×C4 | semidirect |
| 62. C2×Dic178 | C22×C4 | semidirect |
| 77. C4×Dic89 | C22×C4 | semidirect |
| 174. C22×C89 | #354 | semidirect |
| 191. C2×C89 | C2×#354 | semidirect |
| 197. C89 | C22×#354 | semidirect |
| 367. C22 | #19151392 | direct (N × H) |
| 383. C2 | C2×#19151392 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667999 | 2 |
| C22×#15667927 | 2 |
| C2×#19151392 | 2 |
| C22×#99×C89 | 2 |
| C22×#354 | 89 |