Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
434 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 434 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. #17988997 | C4 | semidirect |
| 27. #17988996 | C4 | semidirect |
| 28. #17988993 | C4 | semidirect |
| 34. #501×C73 | C4 | semidirect |
| 210. C73 | #9440 | semidirect |
| 216. #501 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626466 | 2 |
| #22625414 | 2 |
| #22625325 | 2 |
| #22625323 | 2 |
| #22624820 | 2 |
| #22620482 | 2 |
| #9440 | 73 |