Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
396 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 22. #17985740 | C4 | semidirect |
| 179. C71 | #8915 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22591525 | 2 |
| #22589308 | 2 |
| #22588475 | 2 |
| C2×#17985740 | 2 |
| #22586222 | 2 |
| #22586221 | 2 |
| C71×#1836 | 2 |
| #8915 | 71 |