Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
398 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 398 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 |
|---|---|---|
| 12. #17988992 | C4 | semidirect |
| 14. #17988991 | C4 | semidirect |
| 19. #500×C73 | C4 | semidirect |
| 25. #14556660 | Q8 | semidirect |
| 131. C73 | #13275 | semidirect |
| 138. #500 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626261 | 2 |
| C4×#14556660 | 2 |
| #22624988 | 2 |
| #500×D73 | 2 |
| #13275 | 73 |