Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
316 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 60 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. #22626307 | C2 | semidirect |
| 2. #22625653 | C2 | semidirect |
| 3. #22624906 | C2 | semidirect |
| 4. #22624905 | C2 | semidirect |
| 5. #22624902 | C2 | semidirect |
| 6. #22624901 | C2 | semidirect |
| 17. #17988987 | C4 | semidirect |
| 18. #17988962 | C4 | semidirect |
| 23. #17988700 | C4 | semidirect |
| 26. #442×C73 | C4 | semidirect |
| 158. C73 | #11770 | semidirect |
| 167. #442 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626307 | 2 |
| #22625653 | 2 |
| #22624906 | 2 |
| #22624905 | 2 |
| #22624902 | 2 |
| #22624901 | 2 |
| #22620579 | 2 |
| #11770 | 73 |