Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
428 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #22609975 | C2 | semidirect |
| 4. #22608052 | C2 | semidirect |
| 5. C73×#1391 | C2 | semidirect |
| 6. C2×#14556599 | C4 | semidirect |
| 12. #17988610 | C4 | semidirect |
| 14. #17988553 | C4 | semidirect |
| 15. C2×C8×Dic73 | C4 | semidirect |
| 155. #1391 | D73 | semidirect |
| 156. C73 | #12807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618639 | 2 |
| #22611594 | 2 |
| #22609975 | 2 |
| #22608052 | 2 |
| C73×#1391 | 2 |
| #12807 | 73 |