Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
750 conjugacy classes of subgroups; only the 397 normal subgroups are shown.
This group has 750 conjugacy classes of subgroups — too many to draw. Only its 397 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 |
|---|---|---|
| 6. C8×#10596842 | C4 | direct (N × H) |
| 13. C4×#10596842 | C8 | direct (N × H) |
| 19. C4×#10596833 | C8 | semidirect |
| 20. C8×#64408 | C8 | semidirect |
| 24. C4×#10596831 | C8 | semidirect |
| 25. C8×Dic73 | C8 | semidirect |
| 26. C4×C8×C73 | C8 | semidirect |
| 51. #10596842 | C4×C8 | direct (N × H) |
| 59. #10596833 | C4×C8 | semidirect |
| 60. C8×C73 | C4×C8 | semidirect |
| 61. #10596831 | C4×C8 | semidirect |
| 66. #64408 | C82 | semidirect |
| 68. C4×C73 | C82 | semidirect |
| 70. Dic73 | C82 | semidirect |
| 80. C73 | C4×C82 | semidirect |
| 103. C4×C8 | #10596842 | direct (N × H) |
| 138. C8 | C4×#10596842 | direct (N × H) |
| 147. C4 | C8×#10596842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×#10596842 | 2 |
| C2×C8×#10596842 | 2 |
| C4×C8×#64408 | 2 |
| C4×C82 | 73 |