Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
472 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 78 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. #22626776 | C2 | semidirect |
| 2. #22625694 | C2 | semidirect |
| 3. #22625386 | C2 | semidirect |
| 4. #22625320 | C2 | semidirect |
| 5. #22624818 | C2 | semidirect |
| 6. #22624797 | C2 | semidirect |
| 25. #17988873 | C4 | semidirect |
| 26. #17988867 | C4 | semidirect |
| 27. #17988784 | C4 | semidirect |
| 32. #459×C73 | C4 | semidirect |
| 210. C73 | #9162 | semidirect |
| 217. #459 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626776 | 2 |
| #22625694 | 2 |
| #22625386 | 2 |
| #22625320 | 2 |
| #22624818 | 2 |
| #22624797 | 2 |
| #22620079 | 2 |
| #9162 | 73 |