Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
126 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 1. #26011888 | C2 | semidirect |
| 3. #26011314 | C2 | semidirect |
| 4. #26011313 | C2 | semidirect |
| 5. #26011311 | C2 | semidirect |
| 29. Q16×C173 | Q8 | semidirect |
| 31. D8×C173 | Q8 | semidirect |
| 60. C173 | #2230 | semidirect |
| 82. Q16 | Dic346 | semidirect |
| 84. D8 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011888 | 2 |
| #26011608 | 2 |
| #26011314 | 2 |
| #26011313 | 2 |
| #26011311 | 2 |
| #26011301 | 2 |
| #360×C173 | 2 |
| #2230 | 173 |