Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
738 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 135 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. #26020188 | C2 | semidirect |
| 4. #26018120 | C2 | semidirect |
| 10. #19151518 | C4 | semidirect |
| 11. #19151510 | C4 | semidirect |
| 110. C23×C89 | #103 | semidirect |
| 130. C2×C4×C89 | #103 | semidirect |
| 189. C89 | #9467 | semidirect |
| 294. C23 | #15667937 | semidirect |
| 328. C2×C4 | #15667937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023617 | 2 |
| #26020240 | 2 |
| #26020188 | 2 |
| #26018120 | 2 |
| C89×#2972 | 2 |
| #9467 | 89 |