Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
246 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 24. #108×C89 | C8 | semidirect |
| 88. C89 | #7173 | semidirect |
| 107. #108 | #10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667952 | 2 |
| C2×#19151349 | 2 |
| C4×#108×C89 | 2 |
| #7173 | 89 |