Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
280 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 7. #19149747 | C4 | direct (N × H) |
| 12. C4×#13063436 | C4 | semidirect |
| 13. C8×Dic173 | C4 | semidirect |
| 14. C8×Dic173 | C4 | semidirect |
| 15. C4×C8×C173 | C4 | semidirect |
| 45. #13063436 | C42 | semidirect |
| 50. C8×C173 | C42 | semidirect |
| 57. C4×C173 | #106 | semidirect |
| 61. Dic173 | #106 | semidirect |
| 67. C173 | C4×#106 | semidirect |
| 82. C4×C8 | #10621924 | semidirect |
| 118. C8 | C4×#10621924 | semidirect |
| 128. C4 | #19149747 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149747 | 2 |
| C4×C4⋊#10621924 | 2 |
| #26012365 | 2 |
| C4×C8×D173 | 2 |
| C4×#106 | 173 |