Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2222 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2222 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. #26026212 | C2 | direct (N × H) |
| 2. C2×#19151527 | C2 | semidirect |
| 3. C2×#19151522 | C2 | semidirect |
| 5. C2×#19151496 | C2 | semidirect |
| 6. C2×#376×C89 | C2 | semidirect |
| 12. #19151527 | C22 | semidirect |
| 13. #19151522 | C22 | semidirect |
| 15. #19151496 | C22 | semidirect |
| 18. #376×C89 | C22 | semidirect |
| 107. C2×C89 | #2644 | semidirect |
| 117. C2×#376 | D89 | semidirect |
| 118. C89 | C2×#2644 | semidirect |
| 129. #376 | C2×D89 | semidirect |
| 219. C2 | #26026212 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026212 | 2 |
| C2×#19151527 | 2 |
| C2×#19151522 | 2 |
| C2×#19151500 | 2 |
| C2×#19151496 | 2 |
| C2×#376×C89 | 2 |
| C2×#2644 | 89 |