Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
166 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 40 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 |
|---|---|---|
| 5. #19149737 | C4 | semidirect |
| 7. C22×#13063436 | C4 | semidirect |
| 9. C2×M16×C173 | C4 | semidirect |
| 53. C173 | #1391 | semidirect |
| 58. C2×M16 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012470 | 2 |
| #26011459 | 2 |
| #1391 | 173 |