Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
390 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 74 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. #22626838 | C2 | semidirect |
| 2. #22625453 | C2 | semidirect |
| 5. #22624795 | C2 | semidirect |
| 6. #22624787 | C2 | semidirect |
| 199. C73 | #9372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22626838 | 2 |
| #22625453 | 2 |
| #22625421 | 2 |
| #22625238 | 2 |
| #22624795 | 2 |
| #22624787 | 2 |
| #22621130 | 2 |
| #9372 | 73 |