Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
612 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#19149602 | C2 | semidirect |
| 3. C2×#19149599 | C2 | semidirect |
| 4. C2×C22⋊#13063436 | C2 | semidirect |
| 5. #380×C173 | C2 | semidirect |
| 9. C2×#14583826 | C4 | semidirect |
| 60. Dic346 | C22⋊C4 | semidirect |
| 63. D692 | C22⋊C4 | semidirect |
| 115. C173 | #1788 | semidirect |
| 121. #380 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583826 | 2 |
| C2×#19149602 | 2 |
| C2×#19149599 | 2 |
| C2×C22⋊#13063436 | 2 |
| #380×C173 | 2 |
| #1788 | 173 |