Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
402 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 5. C2×#14556660 | C4 | semidirect |
| 7. #17989482 | C4 | semidirect |
| 12. #17988350 | C4 | semidirect |
| 14. #340×C73 | C4 | semidirect |
| 146. C73 | #7258 | semidirect |
| 157. #340 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626156 | 2 |
| #22625808 | 2 |
| #340×D73 | 2 |
| #7258 | 73 |