Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
444 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #26018241 | C2 | semidirect |
| 5. #26018240 | C2 | semidirect |
| 6. #26018239 | C2 | semidirect |
| 7. C89×#1340 | C2 | semidirect |
| 8. C2×Q16×D89 | C4 | semidirect |
| 13. #19151857 | C4 | semidirect |
| 17. #19151853 | C4 | semidirect |
| 18. #106×D89 | C4 | semidirect |
| 29. C2×Dic356 | C2×C4 | semidirect |
| 58. #15667944 | C2×C4 | semidirect |
| 63. C2×Q16×C89 | C2×C4 | semidirect |
| 68. #106×C89 | C2×C4 | semidirect |
| 200. D89 | #1340 | direct (N × H) |
| 207. #1340 | D89 | direct (N × H) |
| 208. C89 | C2×#1340 | semidirect |
| 234. C2×Q16 | C4×D89 | semidirect |
| 266. #106 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #470×D89 | 2 |
| #349×D89 | 2 |
| H(3,ℤ/4)×D89 | 2 |
| #26018241 | 2 |
| #26018240 | 2 |
| #26018239 | 2 |
| C89×#1340 | 2 |
| C2×#1340 | 89 |