Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
218 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 75 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. #26022534 | C2 | semidirect |
| 4. #26018326 | C2 | semidirect |
| 5. #26018309 | C2 | semidirect |
| 6. #26018306 | C2 | semidirect |
| 65. C16×C89 | SD16 | semidirect |
| 110. C89 | #12453 | semidirect |
| 168. C16 | #13083562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022534 | 2 |
| #26019651 | 2 |
| #26019641 | 2 |
| #26018326 | 2 |
| #26018309 | 2 |
| #26018306 | 2 |
| D4×C16×C89 | 2 |
| #12453 | 89 |