Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 109 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×#19149610 | C2 | semidirect |
| 4. #26011254 | C2 | semidirect |
| 5. #340×C173 | C2 | semidirect |
| 9. C2×C8×D173 | C4 | semidirect |
| 48. #13063436 | C22⋊C4 | semidirect |
| 67. C2×D173 | #106 | semidirect |
| 80. C173 | #1807 | semidirect |
| 86. #340 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D173 | 2 |
| C2×#19149610 | 2 |
| #26011348 | 2 |
| #26011254 | 2 |
| #340×C173 | 2 |
| #1807 | 173 |