Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1018 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26031010 | C2 | semidirect |
| 2. C2×#19151749 | C2 | semidirect |
| 4. #26021236 | C2 | semidirect |
| 5. #26018819 | C2 | semidirect |
| 6. #26018099 | C2 | semidirect |
| 7. C89×#1786 | C2 | semidirect |
| 31. C22×Dic178 | D4 | semidirect |
| 51. C2×C4⋊Dic89 | D4 | semidirect |
| 63. C22⋊#10623494 | D4 | semidirect |
| 74. C22×C8×C89 | D4 | semidirect |
| 113. C22⋊Dic89 | SD16 | semidirect |
| 261. #1786 | D89 | semidirect |
| 264. C89 | #9954 | semidirect |
| 305. C22×C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031010 | 2 |
| C2×#19151749 | 2 |
| #26023885 | 2 |
| #26021236 | 2 |
| #26018819 | 2 |
| #26018099 | 2 |
| C89×#1786 | 2 |
| #9954 | 89 |