Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
606 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 606 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26021238 | C2 | semidirect |
| 5. #26018131 | C2 | semidirect |
| 6. #26018099 | C2 | semidirect |
| 7. C2×#328×C89 | C2 | semidirect |
| 11. #19151916 | C4 | semidirect |
| 14. #19151737 | C4 | semidirect |
| 58. C22⋊#10623494 | C2×C4 | semidirect |
| 63. C22×Q8×C89 | C2×C4 | semidirect |
| 72. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 108. C22⋊Dic89 | SD16 | semidirect |
| 255. C2×#328 | D89 | semidirect |
| 258. C89 | #9275 | semidirect |
| 282. C22×Q8 | C4×D89 | semidirect |
| 305. C2×C4⋊C4 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031005 | 2 |
| #26023299 | 2 |
| #26021238 | 2 |
| #26018821 | 2 |
| #26018131 | 2 |
| #26018099 | 2 |
| C2×#328×C89 | 2 |
| #9275 | 89 |