Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
236 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26022504 | C2 | semidirect |
| 4. #26018323 | C2 | semidirect |
| 5. #26018301 | C2 | semidirect |
| 6. #26018300 | C2 | semidirect |
| 77. D4×C89 | Q32 | semidirect |
| 118. C89 | #12431 | semidirect |
| 190. D4 | #15667958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022504 | 2 |
| D4×#13083549 | 2 |
| #26019617 | 2 |
| #26018323 | 2 |
| #26018301 | 2 |
| #26018300 | 2 |
| C89×#1669 | 2 |
| #12431 | 89 |