Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
692 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 261 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. #26011421 | C2 | direct (N × H) |
| 81. C2×C173 | #398 | semidirect |
| 87. C173 | C2×#398 | semidirect |
| 169. C2 | #26011421 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic173 | 2 |
| C22×#14583805 | 2 |
| #26011421 | 2 |
| C2×#19149586 | 2 |
| C22×C4⋊C4×C173 | 2 |
| C2×#398 | 173 |