Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
240 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 58 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. #26012401 | C2 | direct (N × H) |
| 66. C2×C173 | #356 | semidirect |
| 68. C173 | C2×#356 | semidirect |
| 135. C2 | #26012401 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149740 | 2 |
| #26012401 | 2 |
| C2×#19149677 | 2 |
| C2×#356 | 173 |