Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
262 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 84. #10623494 | Q32 | semidirect |
| 105. C89 | #12504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022525 | 2 |
| #26022504 | 2 |
| #26022480 | 2 |
| #26019850 | 2 |
| #26019846 | 2 |
| C16×#10623494 | 2 |
| C89×#2241 | 2 |
| #12504 | 89 |