Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
270 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 152 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. C32×#64408 | C2 | direct (N × H) |
| 7. #17989518 | C4 | semidirect |
| 9. C2×#14556641 | C4 | semidirect |
| 13. C2×#14556497 | C4 | semidirect |
| 14. C32×D73 | C4 | semidirect |
| 16. C2×C32×C73 | C4 | semidirect |
| 24. #14556641 | C2×C4 | semidirect |
| 31. #14556497 | C2×C4 | semidirect |
| 33. C32×C73 | C2×C4 | semidirect |
| 53. C2×#64408 | C32 | direct (N × H) |
| 70. #64408 | C2×C32 | direct (N × H) |
| 76. C2×C73 | C4×C32 | semidirect |
| 78. D73 | C4×C32 | semidirect |
| 84. C73 | C2×C4×C32 | semidirect |
| 94. C2×C32 | #64408 | direct (N × H) |
| 113. C32 | C2×#64408 | direct (N × H) |
| 157. C2 | C32×#64408 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989518 | 2 |
| C2×C16×#64408 | 2 |
| C32×#64408 | 2 |
| C2×C32×D73 | 2 |
| C2×C4×C32 | 73 |