Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
324 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 105 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×#19149608 | C2 | semidirect |
| 5. #26011246 | C2 | semidirect |
| 6. #26011245 | C2 | semidirect |
| 7. C2×C4⋊C8×C173 | C2 | semidirect |
| 72. C2×Dic173 | M16 | semidirect |
| 85. C2×C4×C173 | M16 | semidirect |
| 125. C173 | #1851 | semidirect |
| 129. C2×C4⋊C8 | D173 | semidirect |
| 209. C2×C4 | #14583809 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583809 | 2 |
| C2×#19149608 | 2 |
| C2×#19149591 | 2 |
| C4×#14583803 | 2 |
| #26011246 | 2 |
| #26011245 | 2 |
| C2×C4⋊C8×C173 | 2 |
| #1851 | 173 |