Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 141 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. #17989677 | C4 | semidirect |
| 7. #17989676 | C4 | semidirect |
| 27. #14556645 | C8 | semidirect |
| 35. #14556502 | C8 | semidirect |
| 36. #14556501 | C8 | semidirect |
| 37. #14556501 | C8 | semidirect |
| 38. #97×C73 | C8 | semidirect |
| 113. C73 | #8268 | semidirect |
| 142. #97 | #10596842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22627055 | 2 |
| #22627040 | 2 |
| #22626936 | 2 |
| #97×#64408 | 2 |
| #8268 | 73 |