Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
7034 conjugacy classes of subgroups; only the 675 normal subgroups are shown.
This group has 7034 conjugacy classes of subgroups — too many to draw. Only its 675 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. C25×Dic73 | C2 | semidirect |
| 3. C2×#17988464 | C2 | semidirect |
| 4. #22608153 | C2 | semidirect |
| 5. C2×#379×C73 | C2 | semidirect |
| 12. C2×#14556560 | C4 | semidirect |
| 14. C22×#11924005 | C22 | semidirect |
| 16. C2×#14556498 | C22 | semidirect |
| 25. C22×C22⋊D73 | C2×C4 | semidirect |
| 31. C23×Dic73 | D4 | semidirect |
| 37. C2×C22⋊Dic73 | C2×C4 | semidirect |
| 54. C23×D73 | C22×C4 | semidirect |
| 71. C22×Dic73 | C22×C4 | semidirect |
| 83. C24×C73 | C22⋊C4 | semidirect |
| 135. C2×Dic73 | #120 | semidirect |
| 143. C22×C73 | #386 | semidirect |
| 170. C2×#379 | D73 | semidirect |
| 172. C73 | #14694 | semidirect |
| 230. C24 | #11924005 | semidirect |
| 315. C22 | #17988464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×Dic73 | 2 |
| C22×#14556560 | 2 |
| C2×#17988464 | 2 |
| #22608153 | 2 |
| C2×#379×C73 | 2 |
| #14694 | 73 |