Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
332 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 332 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 |
|---|---|---|
| 4. #26021000 | C2 | semidirect |
| 5. #26018348 | C2 | semidirect |
| 6. #26018346 | C2 | semidirect |
| 7. C2×C4×C16×C89 | C2 | semidirect |
| 16. #19151403 | C4 | semidirect |
| 17. #19151400 | C4 | semidirect |
| 140. C2×C4×C16 | D89 | semidirect |
| 145. C89 | #13151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151406 | 2 |
| #26021960 | 2 |
| #26021140 | 2 |
| #26021000 | 2 |
| #26018348 | 2 |
| #26018346 | 2 |
| C2×C4×C16×C89 | 2 |
| #13151 | 89 |