Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
574 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 233 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 |
|---|---|---|
| 15. C4×#10596842 | C8 | semidirect |
| 21. C4×#10596833 | C8 | semidirect |
| 22. C4×#10596833 | C8 | semidirect |
| 27. C4×#10596831 | C8 | semidirect |
| 28. C8×Dic73 | C8 | semidirect |
| 29. C4×C8×C73 | C8 | semidirect |
| 96. C73 | #8131 | semidirect |
| 122. C4×C8 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×#10596842 | 2 |
| (C2×#10596842)⋊C8 | 2 |
| C4×C8×#64408 | 2 |
| #8131 | 73 |