Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
462 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. C2×#17988386 | C2 | semidirect |
| 5. #22610146 | C2 | semidirect |
| 6. #22608057 | C2 | semidirect |
| 7. C73×#1886 | C2 | semidirect |
| 223. #1886 | D73 | semidirect |
| 226. C73 | #13427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22616937 | 2 |
| C2×#17988386 | 2 |
| C2×#17988383 | 2 |
| #22610334 | 2 |
| #22610146 | 2 |
| #22608057 | 2 |
| C73×#1886 | 2 |
| #13427 | 73 |