Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
824 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 824 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×#19151367 | C2 | semidirect |
| 2. C2×#19151324 | C2 | semidirect |
| 3. #26018255 | C2 | direct (N × H) |
| 8. #19151367 | C22 | semidirect |
| 10. #19151324 | C22 | semidirect |
| 198. C2×C89 | #1345 | semidirect |
| 206. C89 | C2×#1345 | semidirect |
| 399. C2 | #26018255 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151367 | 2 |
| C2×#19151324 | 2 |
| #26018255 | 2 |
| C2×#394×C89 | 2 |
| C2×#1345 | 89 |