Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 2. #26012433 | C2 | semidirect |
| 3. #26012369 | C2 | semidirect |
| 10. C22×C4×D173 | C4 | semidirect |
| 14. C2×C4⋊Dic173 | C4 | semidirect |
| 15. C2×#14583803 | C4 | semidirect |
| 17. C2×C42×C173 | C4 | semidirect |
| 53. C22×D173 | C4⋊C4 | semidirect |
| 76. C2×C4×C173 | C4⋊C4 | semidirect |
| 98. C4×C173 | #99 | semidirect |
| 109. C173 | #1799 | semidirect |
| 125. C2×C42 | #10621924 | semidirect |
| 186. C2×C4 | C4⋊#10621924 | semidirect |
| 210. C4 | #19149738 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149738 | 2 |
| #26012433 | 2 |
| #26012369 | 2 |
| C2×C4×D692 | 2 |
| #1799 | 173 |