Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
1310 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1310 conjugacy classes of subgroups — too many to draw. Only its 232 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×#17989609 | C2 | semidirect |
| 2. #22625411 | C2 | direct (N × H) |
| 3. C2×#17989443 | C2 | semidirect |
| 4. C2×#17989442 | C2 | semidirect |
| 7. #17989609 | C22 | semidirect |
| 10. C2×#14556646 | C22 | semidirect |
| 11. #17989443 | C22 | semidirect |
| 12. #17989442 | C22 | semidirect |
| 29. #14556646 | C23 | semidirect |
| 191. C2×C73 | #1533 | semidirect |
| 201. C73 | C2×#1533 | semidirect |
| 388. C2 | #22625411 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17989609 | 2 |
| #22625411 | 2 |
| C2×#17989443 | 2 |
| C2×#17989442 | 2 |
| C2×#124×D73 | 2 |
| C2×#1533 | 73 |