Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
524 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 1. C2×#19149671 | C2 | semidirect |
| 2. #26011398 | C2 | semidirect |
| 4. #26011385 | C2 | semidirect |
| 5. C42×Dic173 | C2 | semidirect |
| 68. C173 | #2861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149671 | 2 |
| #26011398 | 2 |
| #26011394 | 2 |
| #26011385 | 2 |
| C42×Dic173 | 2 |
| C2×#124×C173 | 2 |
| #2861 | 173 |