Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2664 conjugacy classes of subgroups; only the 1093 normal subgroups are shown.
This group has 2664 conjugacy classes of subgroups — too many to draw. Only its 1093 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. #26023426 | C2 | semidirect |
| 2. #26023393 | C2 | semidirect |
| 3. #124×Dic89 | C2 | semidirect |
| 4. #120×Dic89 | C2 | semidirect |
| 6. C24×Dic89 | C22 | semidirect |
| 7. C2×Q8×Dic89 | C22 | semidirect |
| 9. #19151505 | C22 | semidirect |
| 11. #19151491 | C22 | semidirect |
| 13. #19151473 | C22 | semidirect |
| 14. #19151464 | C22 | semidirect |
| 15. #19151454 | C22 | semidirect |
| 16. C22⋊C4×Dic89 | C22 | semidirect |
| 17. C42×Dic89 | C22 | semidirect |
| 18. H(3,𝔽4)×C89 | C4 | semidirect |
| 36. #124×C89 | C2×C4 | semidirect |
| 37. #120×C89 | C2×C4 | semidirect |
| 54. C24×C89 | C22×C4 | semidirect |
| 58. C2×Q8×C89 | C22×C4 | semidirect |
| 63. C22⋊C4×C89 | C22×C4 | semidirect |
| 64. C42×C89 | C22×C4 | semidirect |
| 93. Dic89 | H(3,𝔽4) | direct (N × H) |
| 104. C89 | C4×H(3,𝔽4) | semidirect |
| 106. H(3,𝔽4) | Dic89 | direct (N × H) |
| 126. #124 | C2×Dic89 | semidirect |
| 127. #120 | C2×Dic89 | semidirect |
| 141. C24 | C22×Dic89 | semidirect |
| 145. C2×Q8 | C22×Dic89 | semidirect |
| 160. C22⋊C4 | C22×Dic89 | semidirect |
| 163. C42 | C22×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023426 | 2 |
| #26023393 | 2 |
| #124×Dic89 | 2 |
| #120×Dic89 | 2 |
| C2×H(3,𝔽4)×C89 | 2 |
| C4×H(3,𝔽4) | 89 |