Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
532 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 15. #17989444 | C4 | semidirect |
| 18. #17988329 | C4 | semidirect |
| 19. #17988328 | C4 | semidirect |
| 20. #330×C73 | C4 | semidirect |
| 112. #64408 | #330 | direct (N × H) |
| 130. C73 | C4×#330 | semidirect |
| 145. #330 | #64408 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #125×#64408 | 2 |
| #97×#64408 | 2 |
| D73⋊#330 | 2 |
| #22624808 | 2 |
| #330×D73 | 2 |
| C4×#330 | 73 |