Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
168 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 82 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. #26012381 | C2 | direct (N × H) |
| 7. #19149754 | C4 | semidirect |
| 9. C2×#14583829 | C4 | semidirect |
| 13. #19149618 | C4 | semidirect |
| 15. C2×#14583801 | C4 | semidirect |
| 16. C2×C16×C173 | C4 | semidirect |
| 23. #14583829 | C2×C4 | semidirect |
| 30. #14583801 | C2×C4 | semidirect |
| 32. C16×C173 | C2×C4 | semidirect |
| 56. C2×C173 | #347 | semidirect |
| 60. C173 | C2×#347 | semidirect |
| 75. C2×C16 | #10621924 | semidirect |
| 93. C16 | C2×#10621924 | semidirect |
| 119. C2 | #26012381 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149754 | 2 |
| C2×#19149733 | 2 |
| #26012381 | 2 |
| C2×#19149618 | 2 |
| C2×#347 | 173 |