Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
842 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 250 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 |
|---|---|---|
| 7. C2×#14556645 | C4 | semidirect |
| 8. C2×C8×#64408 | C4 | semidirect |
| 9. #17989455 | C4 | semidirect |
| 11. #17988345 | C4 | semidirect |
| 12. #338×C73 | C4 | semidirect |
| 94. C73 | #10699 | semidirect |
| 102. #338 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989553 | 2 |
| #22625603 | 2 |
| #338×D73 | 2 |
| #10699 | 73 |