Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
598 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 2. #26018198 | C2 | direct (N × H) |
| 35. C2×C42×C89 | C8 | semidirect |
| 69. C42×C89 | C2×C8 | semidirect |
| 127. C2×C89 | #1325 | semidirect |
| 134. C89 | C2×#1325 | semidirect |
| 164. C2×C42 | #10623494 | semidirect |
| 200. C42 | C2×#10623494 | semidirect |
| 257. C2 | #26018198 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151324 | 2 |
| #26018198 | 2 |
| C2×#384×C89 | 2 |
| C2×#1325 | 89 |