Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
264 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 90 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. #26012507 | C2 | semidirect |
| 2. #26012336 | C2 | semidirect |
| 34. C22×C4×C173 | C8 | semidirect |
| 84. C173 | #1458 | semidirect |
| 110. C22×C4 | #13063443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012507 | 2 |
| #26012336 | 2 |
| #26012334 | 2 |
| C2×#19149638 | 2 |
| #1458 | 173 |