Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
460 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 213 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. #26011538 | C2 | direct (N × H) |
| 4. C2×#19149615 | C2 | semidirect |
| 5. C2×#19149614 | C2 | semidirect |
| 6. C2×#108×C173 | C2 | semidirect |
| 17. #19149615 | C22 | semidirect |
| 18. #19149614 | C22 | semidirect |
| 21. #108×C173 | C22 | semidirect |
| 83. C2×C173 | #430 | semidirect |
| 86. C173 | C2×#430 | semidirect |
| 93. C2×#108 | D173 | semidirect |
| 108. #108 | C2×D173 | semidirect |
| 171. C2 | #26011538 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583809 | 2 |
| C2×M16×D173 | 2 |
| #26011538 | 2 |
| C2×#19149615 | 2 |
| C2×#19149614 | 2 |
| C2×#108×C173 | 2 |
| C2×#430 | 173 |