Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
512 conjugacy classes of subgroups; only the 186 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 186 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 | direct (N × H) |
| 7. C2×C4⋊#10621924 | C4 | semidirect |
| 10. C22×#13063436 | C4 | semidirect |
| 12. C2×C8×D173 | C4 | semidirect |
| 14. C22×C8×C173 | C4 | semidirect |
| 21. C4⋊#10621924 | C2×C4 | semidirect |
| 31. C2×#13063436 | C2×C4 | semidirect |
| 36. C2×C8×C173 | C2×C4 | semidirect |
| 82. C2×C173 | #340 | semidirect |
| 86. D173 | #340 | semidirect |
| 89. C173 | C2×#340 | semidirect |
| 100. C22×C8 | #10621924 | semidirect |
| 123. C2×C8 | C2×#10621924 | semidirect |
| 175. C2 | #26012365 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#10621924 | 2 |
| #26012365 | 2 |
| C22×C8×D173 | 2 |
| C2×#340 | 173 |