Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
398 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 23. #17988334 | C4 | semidirect |
| 24. #17988333 | C4 | semidirect |
| 25. #17988332 | C4 | semidirect |
| 26. #332×C73 | C4 | semidirect |
| 194. C73 | #9565 | semidirect |
| 213. #332 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626112 | 2 |
| #22626097 | 2 |
| #22626043 | 2 |
| #22625724 | 2 |
| #22624810 | 2 |
| #22624760 | 2 |
| #332×D73 | 2 |
| #9565 | 73 |