Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
224 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26022157 | C2 | semidirect |
| 4. #26018230 | C2 | semidirect |
| 6. C8×#13083549 | C2 | semidirect |
| 7. C89×#1367 | C2 | semidirect |
| 59. #13083549 | SD16 | semidirect |
| 84. C8×C89 | M32 | semidirect |
| 109. #1367 | D89 | semidirect |
| 113. C89 | #12051 | semidirect |
| 192. C8 | #15667951 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022157 | 2 |
| #26022083 | 2 |
| C8×#13083563 | 2 |
| #26018230 | 2 |
| #26018206 | 2 |
| C8×#13083549 | 2 |
| C89×#1367 | 2 |
| #12051 | 89 |