Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
454 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 9. #17986378 | C4 | semidirect |
| 10. #17986349 | C4 | semidirect |
| 87. C4×Dic71 | Q16 | semidirect |
| 173. C71 | #9297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599288 | 2 |
| #22591089 | 2 |
| #22589320 | 2 |
| #22586905 | 2 |
| #22586200 | 2 |
| #22586168 | 2 |
| C71×#1548 | 2 |
| #9297 | 71 |