Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26022395 | C2 | semidirect |
| 4. C8×Dic356 | C2 | semidirect |
| 5. #26018306 | C2 | semidirect |
| 7. C89×#1367 | C2 | semidirect |
| 51. Dic356 | SD16 | semidirect |
| 90. C8×C89 | SD32 | semidirect |
| 115. #1367 | D89 | semidirect |
| 118. C89 | #12417 | semidirect |
| 202. C8 | #15667957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022395 | 2 |
| #26022293 | 2 |
| #26019844 | 2 |
| C8×Dic356 | 2 |
| #26018306 | 2 |
| #26018299 | 2 |
| C89×#1367 | 2 |
| #12417 | 89 |