Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
272 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 9. C4⋊#13063436 | C4 | semidirect |
| 11. C4×#13063436 | C4 | semidirect |
| 36. #13063436 | C4⋊C4 | semidirect |
| 58. C4×C173 | #97 | semidirect |
| 68. C173 | #1770 | semidirect |
| 127. C4 | #19149590 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#13063436 | 2 |
| C2×#19149590 | 2 |
| C2×C4×#13063436 | 2 |
| #26011246 | 2 |
| C4×C4⋊C4×C173 | 2 |
| #1770 | 173 |