Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1054 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 1054 conjugacy classes of subgroups — too many to draw. Only its 143 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. #22610726 | C2 | semidirect |
| 3. #22608609 | C2 | semidirect |
| 4. #22608381 | C2 | semidirect |
| 5. C73×#1800 | C2 | semidirect |
| 14. C2×C4⋊#10596831 | C22 | semidirect |
| 16. C2×C4×#10596831 | C22 | semidirect |
| 21. #423×C73 | C22 | semidirect |
| 194. #1800 | D73 | semidirect |
| 197. C73 | #8353 | semidirect |
| 207. #423 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22623695 | 2 |
| #22610726 | 2 |
| #22608609 | 2 |
| #22608381 | 2 |
| C73×#1800 | 2 |
| #8353 | 73 |