Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 86 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. #22626273 | C2 | semidirect |
| 4. #22625851 | C2 | semidirect |
| 5. #22625004 | C2 | semidirect |
| 6. #22624995 | C2 | semidirect |
| 20. #17988699 | C4 | semidirect |
| 21. #17988695 | C4 | semidirect |
| 22. #17988693 | C4 | semidirect |
| 28. #442×C73 | C4 | semidirect |
| 183. C73 | #12828 | semidirect |
| 189. #442 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626273 | 2 |
| #22626252 | 2 |
| #22626246 | 2 |
| #22625851 | 2 |
| #22625004 | 2 |
| #22624995 | 2 |
| #22618813 | 2 |
| #12828 | 73 |