Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
616 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 175 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. C4×#15667923 | C2 | semidirect |
| 3. #26018133 | C2 | semidirect |
| 8. #19151338 | C4 | direct (N × H) |
| 21. #15667923 | C2×C4 | semidirect |
| 130. C4×C89 | #329 | semidirect |
| 142. C89 | C4×#329 | semidirect |
| 268. C4 | #19151338 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#15667923 | 2 |
| C2×#19151338 | 2 |
| #26018133 | 2 |
| C4×#124×C89 | 2 |
| C4×#329 | 89 |