Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 297 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. #26011518 | C2 | semidirect |
| 3. #26011515 | C2 | semidirect |
| 4. C2×C4⋊#13063436 | C2 | semidirect |
| 61. C4×C173 | #131 | semidirect |
| 68. C173 | #2906 | semidirect |
| 130. C4 | #19149686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149686 | 2 |
| #26011518 | 2 |
| #26011515 | 2 |
| C2×C4⋊#13063436 | 2 |
| C4×#41×C173 | 2 |
| #2906 | 173 |