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 |
| 13. C2×#14583805 | C4 | semidirect |
| 14. C2×C22⋊Dic173 | C4 | semidirect |
| 16. C2×C4×Dic173 | C4 | semidirect |
| 17. C23×C4×C173 | C4 | semidirect |
| 61. C2×Dic173 | C4⋊C4 | semidirect |
| 68. C23×C173 | C4⋊C4 | semidirect |
| 97. C4×C173 | #99 | semidirect |
| 109. C173 | #1799 | semidirect |
| 117. C23×C4 | #10621924 | semidirect |
| 164. C23 | C4⋊#10621924 | semidirect |
| 210. C4 | #19149737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149737 | 2 |
| #26012433 | 2 |
| #26012369 | 2 |
| C2×C4×C22⋊D173 | 2 |
| #1799 | 173 |