Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
3342 conjugacy classes of subgroups; only the 739 normal subgroups are shown.
This group has 3342 conjugacy classes of subgroups — too many to draw. Only its 739 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. C2×#19151500 | C2 | semidirect |
| 3. C2×#19151468 | C2 | semidirect |
| 4. C2×C43×C89 | C2 | semidirect |
| 8. C2×#15668009 | C4 | semidirect |
| 34. C2×C42×C89 | D4 | semidirect |
| 59. C42×C89 | C22⋊C4 | semidirect |
| 79. C2×C4×C89 | #127 | semidirect |
| 96. C4×C89 | #390 | semidirect |
| 108. C2×C43 | D89 | semidirect |
| 109. C89 | #14713 | semidirect |
| 138. C2×C42 | D356 | semidirect |
| 164. C42 | #13083551 | semidirect |
| 187. C2×C4 | #15668009 | semidirect |
| 202. C4 | #19151500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668009 | 2 |
| C2×#19151500 | 2 |
| C2×#19151468 | 2 |
| C2×C43×C89 | 2 |
| #14713 | 89 |