Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 123 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. #17989671 | C4 | semidirect |
| 7. C8×#10596842 | C4 | semidirect |
| 23. #14556645 | C8 | semidirect |
| 32. #14556502 | C8 | semidirect |
| 33. #14556501 | C8 | semidirect |
| 34. #14556501 | C8 | semidirect |
| 35. #97×C73 | C8 | semidirect |
| 106. C73 | #8138 | semidirect |
| 131. #97 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627040 | 2 |
| #22626935 | 2 |
| #22626934 | 2 |
| #22625589 | 2 |
| #8138 | 73 |