Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
478 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 26. #17988918 | C4 | semidirect |
| 28. #17988915 | C4 | semidirect |
| 31. #17988743 | C4 | semidirect |
| 34. #451×C73 | C4 | semidirect |
| 243. C73 | #9342 | semidirect |
| 253. #451 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626473 | 2 |
| #22626120 | 2 |
| #22625341 | 2 |
| #22625329 | 2 |
| #22624833 | 2 |
| #22624780 | 2 |
| #22620753 | 2 |
| #9342 | 73 |