Finite Group DatabasebetaFinite Group DatabasebetaOrder 18688.
632 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 72 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. C4×#14556651 | C2 | semidirect |
| 2. #22625166 | C2 | semidirect |
| 3. #22624932 | C2 | semidirect |
| 4. #22624913 | C2 | semidirect |
| 213. C73 | #11733 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556651 | 2 |
| #22625166 | 2 |
| #22624932 | 2 |
| #22624913 | 2 |
| #22613144 | 2 |
| #11733 | 73 |