Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
294 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 37 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. #26011215 | C2 | semidirect |
| 3. #323×C173 | C2 | semidirect |
| 17. C23×D173 | C8 | semidirect |
| 94. C173 | #1316 | semidirect |
| 98. #323 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011346 | 2 |
| #26011215 | 2 |
| #323×C173 | 2 |
| #1316 | 173 |