Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
446 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26026424 | C2 | semidirect |
| 5. #26018157 | C2 | semidirect |
| 6. #26018138 | C2 | semidirect |
| 7. C89×#1284 | C2 | semidirect |
| 28. C22×D356 | Q8 | semidirect |
| 37. C2×C4⋊Dic89 | Q8 | semidirect |
| 216. #1284 | D89 | semidirect |
| 217. C89 | #10382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026424 | 2 |
| #26021088 | 2 |
| #26018780 | 2 |
| #26018769 | 2 |
| #26018157 | 2 |
| #26018138 | 2 |
| C89×#1284 | 2 |
| #10382 | 89 |