Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 10. Q8×Dic173 | C4 | semidirect |
| 17. #19149603 | C4 | semidirect |
| 23. #103×C173 | C4 | semidirect |
| 71. Q8×C173 | C42 | semidirect |
| 109. C173 | #1763 | semidirect |
| 131. #103 | Dic173 | semidirect |
| 168. Q8 | C4×Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic173 | 2 |
| C2×#19149603 | 2 |
| C2×#19149589 | 2 |
| C4⋊C4×Dic173 | 2 |
| #26011254 | 2 |
| #26011253 | 2 |
| C2×#103×C173 | 2 |
| #1763 | 173 |