Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #26018200 | C2 | semidirect |
| 4. #26018182 | C2 | semidirect |
| 35. #123×C89 | C8 | semidirect |
| 85. C22×C4×C89 | C2×C8 | semidirect |
| 97. C22⋊C4×C89 | C2×C8 | semidirect |
| 193. C89 | #11472 | semidirect |
| 218. #123 | #10623494 | semidirect |
| 270. C22×C4 | C2×#10623494 | semidirect |
| 285. C22⋊C4 | C2×#10623494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26018573 | 2 |
| #26018570 | 2 |
| #26018200 | 2 |
| #26018182 | 2 |
| C4×#123×C89 | 2 |
| #11472 | 89 |