Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
5838 conjugacy classes of subgroups; only the 1339 normal subgroups are shown.
This group has 5838 conjugacy classes of subgroups — too many to draw. Only its 1339 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. C23×#13083553 | C2 | semidirect |
| 3. C2×#19151522 | C2 | direct (N × H) |
| 4. C22×#95×C89 | C2 | semidirect |
| 8. C22×#13083553 | C22 | semidirect |
| 11. #19151522 | C22 | direct (N × H) |
| 13. C2×#95×C89 | C22 | semidirect |
| 23. C2×#13083553 | C23 | semidirect |
| 31. #95×C89 | C23 | semidirect |
| 77. C22×C89 | #396 | semidirect |
| 91. C2×C89 | C2×#396 | semidirect |
| 99. C22×#95 | D89 | semidirect |
| 100. C89 | C22×#396 | semidirect |
| 109. C2×#95 | C2×D89 | semidirect |
| 127. #95 | C22×D89 | semidirect |
| 177. C22 | #19151522 | direct (N × H) |
| 187. C2 | C2×#19151522 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#13083553 | 2 |
| C23×#13083551 | 2 |
| C2×#19151522 | 2 |
| C22×#95×C89 | 2 |
| C22×#396 | 89 |