Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
330 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 161 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. #26011620 | C2 | semidirect |
| 3. #26011619 | C2 | semidirect |
| 4. C8×Dic346 | C2 | semidirect |
| 5. #26011615 | C2 | semidirect |
| 91. C173 | #2986 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012044 | 2 |
| #26011620 | 2 |
| #26011619 | 2 |
| C8×Dic346 | 2 |
| #26011615 | 2 |
| #26011552 | 2 |
| #26011549 | 2 |
| #26011541 | 2 |
| #433×C173 | 2 |
| #2986 | 173 |