Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
216 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 122 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 |
|---|---|---|
| 3. C16×#10621924 | C2 | direct (N × H) |
| 7. D173⋊C16 | C4 | semidirect |
| 9. C2×#14583829 | C4 | semidirect |
| 13. C2×#14583801 | C4 | semidirect |
| 14. C16×D173 | C4 | semidirect |
| 16. C2×C16×C173 | C4 | semidirect |
| 23. #14583829 | C2×C4 | semidirect |
| 30. #14583801 | C2×C4 | semidirect |
| 32. C16×C173 | C2×C4 | semidirect |
| 33. C2×#10621924 | C16 | direct (N × H) |
| 51. #10621924 | C2×C16 | direct (N × H) |
| 56. C2×C173 | C4×C16 | semidirect |
| 58. D173 | C4×C16 | semidirect |
| 60. C173 | C2×C4×C16 | semidirect |
| 75. C2×C16 | #10621924 | direct (N × H) |
| 93. C16 | C2×#10621924 | direct (N × H) |
| 119. C2 | C16×#10621924 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D173⋊C16 | 2 |
| C2×C8×#10621924 | 2 |
| C16×#10621924 | 2 |
| C2×C16×D173 | 2 |
| C2×C4×C16 | 173 |