Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
316 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 11. #19149608 | C4 | direct (N × H) |
| 24. C4×Dic173 | C8 | semidirect |
| 55. C4×C173 | C4⋊C8 | semidirect |
| 60. Dic173 | C4×C8 | semidirect |
| 66. C173 | C4×C4⋊C8 | semidirect |
| 125. C4 | #19149608 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149608 | 2 |
| C2×C4×#13063436 | 2 |
| C42×Dic173 | 2 |
| #26011245 | 2 |
| C2×C4×C8×C173 | 2 |
| C4×C4⋊C8 | 173 |