Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
404 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 128 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. #26012359 | C2 | semidirect |
| 6. #19149758 | C4 | semidirect |
| 10. C2×C4×#10621924 | C4 | semidirect |
| 12. C2×#14583810 | C4 | semidirect |
| 16. C2×C8×D173 | C4 | semidirect |
| 17. C2×M16×C173 | C4 | semidirect |
| 24. C4×#10621924 | C2×C4 | semidirect |
| 37. C2×#13063436 | C2×C4 | semidirect |
| 42. C2×C8×C173 | C2×C4 | semidirect |
| 93. D173 | H(3,ℤ/4) | semidirect |
| 94. C173 | C2×H(3,ℤ/4) | semidirect |
| 104. C2×M16 | #10621924 | semidirect |
| 131. C2×C8 | C2×#10621924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149758 | 2 |
| #26012359 | 2 |
| C2×M16×D173 | 2 |
| C2×H(3,ℤ/4) | 173 |