Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
648 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 100 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. C2×#17989532 | C2 | semidirect |
| 2. #22625823 | C2 | semidirect |
| 4. #22624804 | C2 | semidirect |
| 17. #17988489 | C4 | semidirect |
| 18. #17988488 | C4 | semidirect |
| 19. #17988483 | C4 | semidirect |
| 24. #389×C73 | C4 | semidirect |
| 226. C73 | #9157 | semidirect |
| 234. #389 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989532 | 2 |
| #22625823 | 2 |
| C2×#17989439 | 2 |
| #22624804 | 2 |
| #22618264 | 2 |
| #9157 | 73 |