Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
272 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
| 15. C4×C8×C173 | C4 | semidirect |
| 50. C8×C173 | C4⋊C4 | semidirect |
| 57. C4×C173 | #97 | semidirect |
| 68. C173 | #1770 | semidirect |
| 83. C4×C8 | Dic173 | semidirect |
| 119. C8 | C4⋊Dic173 | semidirect |
| 127. C4 | #19149589 | 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×#19149589 | 2 |
| C4×C4⋊Dic173 | 2 |
| #26011245 | 2 |
| C2×C4×C8×C173 | 2 |
| #1770 | 173 |