Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
172 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. #26022531 | C2 | semidirect |
| 4. #26018312 | C2 | semidirect |
| 5. C89×#1373 | C2 | semidirect |
| 74. #1373 | D89 | semidirect |
| 76. C89 | #12464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022531 | 2 |
| #26022429 | 2 |
| #26022090 | 2 |
| #26018312 | 2 |
| C89×#1373 | 2 |
| #12464 | 89 |