Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
256 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 16. C4⋊#13063436 | C4 | semidirect |
| 17. #19149608 | C4 | semidirect |
| 18. C4⋊C8×C173 | C4 | semidirect |
| 79. C4×C173 | #107 | semidirect |
| 83. Dic173 | #107 | semidirect |
| 93. C173 | #1947 | semidirect |
| 111. C4⋊C8 | #10621924 | semidirect |
| 177. C4 | #19149748 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149748 | 2 |
| #26012437 | 2 |
| C4×C4⋊#10621924 | 2 |
| #26012365 | 2 |
| C4⋊C8×D173 | 2 |
| #1947 | 173 |