Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
358 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 125 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. #26011871 | C2 | semidirect |
| 3. #26011843 | C2 | semidirect |
| 5. #26011597 | C2 | semidirect |
| 7. #498×C173 | C2 | semidirect |
| 68. C173 | #3185 | semidirect |
| 71. #498 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012046 | 2 |
| #26011871 | 2 |
| #26011843 | 2 |
| #26011750 | 2 |
| #26011597 | 2 |
| C4×#14583809 | 2 |
| #498×C173 | 2 |
| #3185 | 173 |