Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
396 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 129 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×#19149591 | C2 | semidirect |
| 3. C2×C4×#13063436 | C2 | semidirect |
| 4. C2×C4⋊C8×C173 | C2 | semidirect |
| 20. C2×D692 | C8 | semidirect |
| 28. C2×#13063436 | D4 | semidirect |
| 72. C4×C173 | C22⋊C8 | semidirect |
| 83. C173 | #1954 | semidirect |
| 86. C2×C4⋊C8 | D173 | semidirect |
| 157. C4 | #19149591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D692 | 2 |
| C2×#19149591 | 2 |
| C2×C4×#13063436 | 2 |
| C2×C4⋊C8×C173 | 2 |
| #1954 | 173 |