Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
694 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 112 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×#17989605 | C2 | semidirect |
| 3. #22625107 | C2 | semidirect |
| 4. #22624804 | C2 | semidirect |
| 17. #17988490 | C4 | semidirect |
| 18. #17988486 | C4 | semidirect |
| 19. #17988485 | C4 | semidirect |
| 24. #390×C73 | C4 | semidirect |
| 233. C73 | #9114 | semidirect |
| 242. #390 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989605 | 2 |
| C2×#17989438 | 2 |
| #22625107 | 2 |
| #22624804 | 2 |
| #22618261 | 2 |
| #9114 | 73 |