Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
256 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19149589 | C4 | semidirect |
| 52. #13063436 | C4⋊C4 | semidirect |
| 64. C8×C173 | C4⋊C4 | semidirect |
| 84. C173 | #1847 | semidirect |
| 149. C8 | #14583805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149613 | 2 |
| C2×#19149612 | 2 |
| C2×#19149610 | 2 |
| C2×#19149589 | 2 |
| #26011360 | 2 |
| #26011356 | 2 |
| C2×#106×C173 | 2 |
| #1847 | 173 |