Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
216 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. #26011306 | C2 | direct (N × H) |
| 71. C2×C173 | #362 | semidirect |
| 73. C173 | C2×#362 | semidirect |
| 145. C2 | #26011306 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic692 | 2 |
| C2×#19149619 | 2 |
| #26011306 | 2 |
| C2×#108×C173 | 2 |
| C2×#362 | 173 |