Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
488 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 25. #17988334 | C4 | semidirect |
| 26. #17988333 | C4 | semidirect |
| 27. #17988332 | C4 | semidirect |
| 28. #332×C73 | C4 | semidirect |
| 210. C73 | #8923 | semidirect |
| 231. #332 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626460 | 2 |
| #22626112 | 2 |
| #22626043 | 2 |
| #22626042 | 2 |
| #22624765 | 2 |
| #332×D73 | 2 |
| #8923 | 73 |