Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
170 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 170 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. #26011217 | C2 | semidirect |
| 3. #324×C173 | C2 | semidirect |
| 15. C2×D692 | C8 | semidirect |
| 72. C173 | #1318 | semidirect |
| 76. #324 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011392 | 2 |
| #26011217 | 2 |
| #324×C173 | 2 |
| #1318 | 173 |