Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
452 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22609734 | C2 | semidirect |
| 4. #22608061 | C2 | semidirect |
| 6. C2×#14556598 | C4 | semidirect |
| 10. #17988611 | C4 | semidirect |
| 12. #17988554 | C4 | semidirect |
| 15. C2×#14556502 | C4 | semidirect |
| 21. #356×C73 | C4 | semidirect |
| 22. #355×C73 | C4 | semidirect |
| 152. C73 | #12634 | semidirect |
| 165. #356 | Dic73 | semidirect |
| 166. #355 | Dic73 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22618649 | 2 |
| #22611596 | 2 |
| #22609734 | 2 |
| #22608061 | 2 |
| C73×#2132 | 2 |
| #12634 | 73 |