Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26019868 | C2 | semidirect |
| 5. #26018315 | C2 | semidirect |
| 6. #26018300 | C2 | semidirect |
| 7. C89×#1362 | C2 | semidirect |
| 95. #10623494 | SD32 | semidirect |
| 119. #1362 | D89 | semidirect |
| 120. C89 | #12493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022298 | 2 |
| #26022294 | 2 |
| #26019868 | 2 |
| #26019136 | 2 |
| #26018315 | 2 |
| #26018300 | 2 |
| C89×#1362 | 2 |
| #12493 | 89 |