Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
224 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 69 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. #26022527 | C2 | semidirect |
| 4. #26018308 | C2 | semidirect |
| 5. C89×#1371 | C2 | semidirect |
| 49. C16×C89 | SD16 | semidirect |
| 86. #1371 | D89 | semidirect |
| 88. C89 | #12451 | semidirect |
| 132. C16 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022527 | 2 |
| C16×D356 | 2 |
| #26019642 | 2 |
| #26018308 | 2 |
| C89×#1371 | 2 |
| #12451 | 89 |