Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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. #26011858 | C2 | direct (N × H) |
| 96. C2×C173 | #491 | semidirect |
| 100. C173 | C2×#491 | semidirect |
| 197. C2 | #26011858 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149677 | 2 |
| C2×#19149670 | 2 |
| #26011858 | 2 |
| C2×#19149604 | 2 |
| C2×#19149603 | 2 |
| C2×#19149602 | 2 |
| C2×#19149589 | 2 |
| C2×#103×C173 | 2 |
| C2×#491 | 173 |