Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
434 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 2. #22625816 | C2 | semidirect |
| 3. #22625814 | C2 | semidirect |
| 4. #22625032 | C2 | semidirect |
| 15. C23×#10596831 | C4 | semidirect |
| 21. #17988615 | C4 | semidirect |
| 23. #17988545 | C4 | semidirect |
| 24. #407×C73 | C4 | semidirect |
| 192. C73 | #12805 | semidirect |
| 206. #407 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626182 | 2 |
| #22625816 | 2 |
| #22625814 | 2 |
| #22625032 | 2 |
| #22618621 | 2 |
| #12805 | 73 |