Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
132 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 132 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 |
|---|---|---|
| 3. #26011316 | C2 | semidirect |
| 4. #26011296 | C2 | semidirect |
| 5. #26011294 | C2 | semidirect |
| 7. #367×C173 | C2 | semidirect |
| 65. C173 | #2237 | semidirect |
| 69. #367 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011733 | 2 |
| #26011528 | 2 |
| #26011316 | 2 |
| #26011296 | 2 |
| #26011294 | 2 |
| #26011270 | 2 |
| #367×C173 | 2 |
| #2237 | 173 |