Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
412 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 1. C22×#14583810 | C2 | semidirect |
| 3. C2×#19149599 | C2 | semidirect |
| 4. #26011253 | C2 | semidirect |
| 5. #380×C173 | C2 | semidirect |
| 12. #19149653 | C4 | semidirect |
| 31. C2×#13063436 | D4 | semidirect |
| 104. C173 | #1895 | semidirect |
| 109. #380 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583810 | 2 |
| C2×#19149653 | 2 |
| C2×#19149599 | 2 |
| #26011253 | 2 |
| #380×C173 | 2 |
| #1895 | 173 |