Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 2. #26021240 | C2 | semidirect |
| 4. #26018934 | C2 | semidirect |
| 6. C8×#13083558 | C2 | semidirect |
| 7. C89×#1566 | C2 | semidirect |
| 79. #13083558 | SD16 | semidirect |
| 129. C8×C89 | #100 | semidirect |
| 157. #1566 | D89 | semidirect |
| 161. C89 | #9793 | semidirect |
| 285. C8 | #15667928 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151971 | 2 |
| #26021240 | 2 |
| #26021091 | 2 |
| #26018934 | 2 |
| #26018921 | 2 |
| C8×#13083558 | 2 |
| C89×#1566 | 2 |
| #9793 | 89 |