Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
326 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 13. #17989480 | C4 | semidirect |
| 14. #17989479 | C4 | semidirect |
| 17. #17988365 | C4 | semidirect |
| 18. #17988364 | C4 | semidirect |
| 19. #347×C73 | C4 | semidirect |
| 115. C73 | #12595 | semidirect |
| 129. #347 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626148 | 2 |
| #97×#64408 | 2 |
| #22624977 | 2 |
| #22624974 | 2 |
| #347×D73 | 2 |
| #12595 | 73 |