Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
396 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 197. C89 | #10385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026449 | 2 |
| #26021236 | 2 |
| #26018786 | 2 |
| #26018773 | 2 |
| #26018137 | 2 |
| #26018106 | 2 |
| C89×#1305 | 2 |
| #10385 | 89 |