Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
442 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#19151419 | C2 | semidirect |
| 2. #26018293 | C2 | direct (N × H) |
| 6. #19151419 | C22 | semidirect |
| 111. C2×C89 | #1359 | semidirect |
| 116. C89 | C2×#1359 | semidirect |
| 223. C2 | #26018293 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151419 | 2 |
| #26018293 | 2 |
| C2×#492×C89 | 2 |
| C2×#1359 | 89 |