Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
504 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 131 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. #22601325 | C2 | semidirect |
| 2. #22590610 | C2 | semidirect |
| 3. #22590399 | C2 | semidirect |
| 5. #22590388 | C2 | semidirect |
| 6. #22590248 | C2 | semidirect |
| 7. #22590205 | C2 | semidirect |
| 8. C4×Dic568 | C2 | semidirect |
| 153. C71 | #33969 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601325 | 2 |
| #22590610 | 2 |
| #22590399 | 2 |
| #22590393 | 2 |
| #22590388 | 2 |
| #22590248 | 2 |
| #22590205 | 2 |
| C4×Dic568 | 2 |
| C71×#2249 | 2 |
| #33969 | 71 |