Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
686 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22608245 | C2 | semidirect |
| 3. #22607862 | C2 | semidirect |
| 4. C73×#1458 | C2 | semidirect |
| 14. #17988313 | C22 | semidirect |
| 18. #324×C73 | C22 | semidirect |
| 26. C22×D292 | C8 | semidirect |
| 183. #1458 | D73 | semidirect |
| 185. C73 | #11433 | semidirect |
| 198. #324 | C2×D73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22612511 | 2 |
| #22608245 | 2 |
| #22607862 | 2 |
| C73×#1458 | 2 |
| #11433 | 73 |