Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26022024 | C2 | semidirect |
| 4. #26018368 | C2 | semidirect |
| 11. #19151380 | C4 | semidirect |
| 21. #15667952 | C2×C4 | semidirect |
| 126. C89 | #12932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022024 | 2 |
| C2×#19151380 | 2 |
| #26020294 | 2 |
| #26018368 | 2 |
| C89×#2911 | 2 |
| #12932 | 89 |