Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
504 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. #26011258 | C2 | semidirect |
| 7. C23×C4×C173 | C4 | semidirect |
| 9. C2×C22⋊C4×C173 | C4 | semidirect |
| 68. C173 | #1819 | semidirect |
| 74. C23×C4 | Dic173 | semidirect |
| 78. C2×C22⋊C4 | Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011347 | 2 |
| #26011258 | 2 |
| C22×C22⋊C4×C173 | 2 |
| #1819 | 173 |