Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
492 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 293 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. #26011533 | C2 | semidirect |
| 3. #26011529 | C2 | semidirect |
| 12. #19149613 | C22 | semidirect |
| 13. #19149611 | C22 | semidirect |
| 15. C2×M16×C173 | C4 | semidirect |
| 32. M16×C173 | C2×C4 | semidirect |
| 33. C2×C8×C173 | C2×C4 | semidirect |
| 66. C173 | #2911 | semidirect |
| 73. C2×M16 | Dic173 | semidirect |
| 93. M16 | C2×Dic173 | semidirect |
| 94. C2×C8 | C2×Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149638 | 2 |
| #26011533 | 2 |
| #26011529 | 2 |
| C22×M16×C173 | 2 |
| #2911 | 173 |