Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
872 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 233 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. C2×#19149644 | C2 | semidirect |
| 3. #26011392 | C2 | semidirect |
| 4. #26011391 | C2 | semidirect |
| 5. #26011350 | C2 | semidirect |
| 6. C4×C22⋊Dic173 | C2 | semidirect |
| 7. #26011338 | C2 | semidirect |
| 8. #380×C173 | C2 | semidirect |
| 10. C2×#14583826 | C4 | semidirect |
| 60. Dic346 | C22⋊C4 | semidirect |
| 70. C2×Dic173 | #41 | semidirect |
| 114. C173 | #2341 | semidirect |
| 121. #380 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583826 | 2 |
| C2×#19149644 | 2 |
| #26011392 | 2 |
| #26011391 | 2 |
| #26011350 | 2 |
| C4×C22⋊Dic173 | 2 |
| #26011338 | 2 |
| #380×C173 | 2 |
| #2341 | 173 |