Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
424 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 138 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. #26012365 | C2 | semidirect |
| 5. #19149758 | C4 | semidirect |
| 10. C22×#13063436 | C4 | semidirect |
| 12. C2×C8×D173 | C4 | semidirect |
| 14. C22×C8×C173 | C4 | semidirect |
| 76. C173 | #1735 | semidirect |
| 86. C22×C8 | #10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149758 | 2 |
| #26012365 | 2 |
| C22×C8×D173 | 2 |
| #1735 | 173 |