Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
136 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 49 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. #26011892 | C2 | semidirect |
| 3. #26011319 | C2 | semidirect |
| 4. #26011316 | C2 | semidirect |
| 5. #26011309 | C2 | semidirect |
| 62. C173 | #2228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011892 | 2 |
| D8×Dic173 | 2 |
| #26011319 | 2 |
| #26011316 | 2 |
| #26011309 | 2 |
| #26011292 | 2 |
| #357×C173 | 2 |
| #2228 | 173 |