Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
470 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 84 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. #22626828 | C2 | semidirect |
| 2. #22625802 | C2 | semidirect |
| 5. #22624821 | C2 | semidirect |
| 6. #22624786 | C2 | semidirect |
| 27. #17988798 | C4 | semidirect |
| 28. #17988797 | C4 | semidirect |
| 29. #17988784 | C4 | semidirect |
| 32. #460×C73 | C4 | semidirect |
| 225. C73 | #9310 | semidirect |
| 234. #460 | #64408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626828 | 2 |
| #22625802 | 2 |
| #22625360 | 2 |
| #22625237 | 2 |
| #22624821 | 2 |
| #22624786 | 2 |
| #22619398 | 2 |
| #9310 | 73 |