Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
152 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #26011312 | C2 | semidirect |
| 4. #26011311 | C2 | semidirect |
| 5. #364×C173 | C2 | semidirect |
| 54. C173 | #2153 | semidirect |
| 60. #364 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M32×D173 | 2 |
| #26011445 | 2 |
| #26011312 | 2 |
| #26011311 | 2 |
| #364×C173 | 2 |
| #2153 | 173 |