Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
302 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26011531 | C2 | semidirect |
| 4. #26011360 | C2 | semidirect |
| 5. #26011259 | C2 | semidirect |
| 6. #26011252 | C2 | semidirect |
| 20. #19149606 | C4 | semidirect |
| 30. #14583810 | C2×C4 | semidirect |
| 43. C4×Dic173 | C2×C4 | semidirect |
| 71. Q8×C173 | C4⋊C4 | semidirect |
| 75. D4×C173 | C4⋊C4 | semidirect |
| 112. C173 | #1859 | semidirect |
| 175. Q8 | #14583805 | semidirect |
| 179. D4 | #14583805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011974 | 2 |
| #26011531 | 2 |
| C2×#19149606 | 2 |
| #26011360 | 2 |
| #26011259 | 2 |
| #26011252 | 2 |
| #417×C173 | 2 |
| #1859 | 173 |