Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
954 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 268 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. #17989523 | C4 | semidirect |
| 8. C42×#64408 | C4 | semidirect |
| 9. #17989455 | C4 | direct (N × H) |
| 13. C2×#14556501 | C4 | semidirect |
| 14. C2×C4×#10596831 | C4 | semidirect |
| 15. C2×C4×C8×C73 | C4 | semidirect |
| 44. C4×#64408 | C42 | semidirect |
| 58. C2×#10596831 | C42 | semidirect |
| 67. C2×C8×C73 | C42 | semidirect |
| 103. C4×C73 | H(3,ℤ/4) | semidirect |
| 117. C73 | C4×H(3,ℤ/4) | semidirect |
| 124. C2×C4×C8 | #64408 | semidirect |
| 172. C2×C8 | C4×#64408 | semidirect |
| 219. C4 | #17989455 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556670 | 2 |
| C2×#17989455 | 2 |
| C2×C4×#11924011 | 2 |
| C4×H(3,ℤ/4) | 73 |