Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
360 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 90 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×#19149746 | C2 | semidirect |
| 2. #26012349 | C2 | direct (N × H) |
| 6. #19149746 | C22 | semidirect |
| 70. C2×C173 | #331 | semidirect |
| 74. C173 | C2×#331 | semidirect |
| 146. C2 | #26012349 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149746 | 2 |
| #26012349 | 2 |
| C2×#19149675 | 2 |
| C2×#331 | 173 |