Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1806 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 1806 conjugacy classes of subgroups — too many to draw. Only its 667 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. #26028521 | C2 | direct (N × H) |
| 41. C2×C42×C89 | Q8 | semidirect |
| 64. C42×C89 | C2×Q8 | semidirect |
| 96. C2×C89 | #2843 | semidirect |
| 106. C89 | C2×#2843 | semidirect |
| 137. C2×C42 | Dic178 | semidirect |
| 164. C42 | C2×Dic178 | semidirect |
| 195. C2 | #26028521 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028521 | 2 |
| C2×#19151537 | 2 |
| C2×#19151531 | 2 |
| C2×#19151518 | 2 |
| C2×#19151466 | 2 |
| C2×#384×C89 | 2 |
| C2×#2843 | 89 |