Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
400 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 96 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. #22625651 | C2 | semidirect |
| 4. #22625129 | C2 | semidirect |
| 5. #22624825 | C2 | semidirect |
| 6. #22624820 | C2 | semidirect |
| 8. #17989637 | C4 | semidirect |
| 9. #17989636 | C4 | semidirect |
| 10. #17989621 | C4 | semidirect |
| 13. #17989615 | C4 | semidirect |
| 29. #17988329 | C4 | semidirect |
| 30. #17988326 | C4 | semidirect |
| 31. #17988326 | C4 | semidirect |
| 32. #330×C73 | C4 | semidirect |
| 185. C73 | #8250 | semidirect |
| 204. #330 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626748 | 2 |
| #22625651 | 2 |
| #22625305 | 2 |
| #22625129 | 2 |
| #22624825 | 2 |
| #22624820 | 2 |
| #22608518 | 2 |
| #8250 | 73 |