Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
4830 conjugacy classes of subgroups; only the 763 normal subgroups are shown.
This group has 4830 conjugacy classes of subgroups — too many to draw. Only its 763 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. #26018523 | C2 | semidirect |
| 4. #26018522 | C2 | semidirect |
| 5. C89×#1446 | C2 | semidirect |
| 8. C22×Q8×D89 | C4 | semidirect |
| 19. C22×Dic178 | C2×C4 | semidirect |
| 29. C22×C4×D89 | Q8 | semidirect |
| 33. C22×Q8×C89 | C2×C4 | semidirect |
| 50. C22×Dic89 | C2×Q8 | semidirect |
| 65. C22×C4×C89 | C2×Q8 | semidirect |
| 111. D89 | #1446 | direct (N × H) |
| 116. #1446 | D89 | direct (N × H) |
| 117. C89 | C2×#1446 | semidirect |
| 135. C22×Q8 | C4×D89 | semidirect |
| 177. C22×C4 | Q8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Q8×D89 | 2 |
| C2×#95×D89 | 2 |
| #26018523 | 2 |
| #26018522 | 2 |
| C89×#1446 | 2 |
| C2×#1446 | 89 |