Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
308 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 125 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×Dic346 | C4 | semidirect |
| 47. Dic346 | C4⋊C4 | semidirect |
| 80. C4×C173 | #103 | semidirect |
| 94. C173 | #1803 | semidirect |
| 177. C4 | #19149602 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic346 | 2 |
| C2×C4⋊#13063436 | 2 |
| C2×#19149602 | 2 |
| #26011253 | 2 |
| #384×C173 | 2 |
| #1803 | 173 |