Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 178. C89 | #11736 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023542 | 2 |
| #26020047 | 2 |
| #26018574 | 2 |
| #26018282 | 2 |
| #26018259 | 2 |
| #26018257 | 2 |
| C89×#1354 | 2 |
| #11736 | 89 |