Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
342 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 63 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 |
|---|---|---|
| 1. #22611864 | C2 | semidirect |
| 3. #22611199 | C2 | semidirect |
| 4. #22607949 | C2 | semidirect |
| 6. #22607873 | C2 | semidirect |
| 167. C73 | #12169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22611864 | 2 |
| #22611847 | 2 |
| #22611199 | 2 |
| #22607949 | 2 |
| #22607946 | 2 |
| #22607873 | 2 |
| C73×#3262 | 2 |
| #12169 | 73 |