Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
350 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 4. #26018311 | C2 | semidirect |
| 5. #26018310 | C2 | semidirect |
| 6. #26018309 | C2 | semidirect |
| 7. C89×#1365 | C2 | semidirect |
| 126. D89 | #1365 | direct (N × H) |
| 133. #1365 | D89 | direct (N × H) |
| 134. C89 | C2×#1365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×D89 | 2 |
| C4⋊C16×D89 | 2 |
| #335×D89 | 2 |
| #26018311 | 2 |
| #26018310 | 2 |
| #26018309 | 2 |
| C89×#1365 | 2 |
| C2×#1365 | 89 |