Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1134 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 371 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. #26020395 | C2 | semidirect |
| 3. #26020394 | C2 | semidirect |
| 5. C89×#1839 | C2 | semidirect |
| 31. C42×D89 | C8 | semidirect |
| 55. C4×Dic89 | C2×C8 | semidirect |
| 62. C42×C89 | C2×C8 | semidirect |
| 102. D89 | #1839 | direct (N × H) |
| 106. #1839 | D89 | direct (N × H) |
| 108. C89 | C2×#1839 | semidirect |
| 165. C42 | C8×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×D89 | 2 |
| #26020395 | 2 |
| #26020394 | 2 |
| #336×D89 | 2 |
| C89×#1839 | 2 |
| C2×#1839 | 89 |