Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
134 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 134 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 |
|---|---|---|
| 2. #26011540 | C2 | semidirect |
| 3. #26011314 | C2 | semidirect |
| 4. #26011305 | C2 | semidirect |
| 5. #349×C173 | C2 | semidirect |
| 55. C173 | #2238 | semidirect |
| 61. #349 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011744 | 2 |
| #26011540 | 2 |
| #26011314 | 2 |
| #26011305 | 2 |
| #349×C173 | 2 |
| #2238 | 173 |