Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
542 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. #22596717 | C2 | semidirect |
| 5. #22587026 | C2 | semidirect |
| 6. #22586172 | C2 | semidirect |
| 7. C71×#1546 | C2 | semidirect |
| 179. #1546 | D71 | semidirect |
| 181. C71 | #10286 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599470 | 2 |
| #22599461 | 2 |
| #22596717 | 2 |
| #22589167 | 2 |
| #22587026 | 2 |
| #22586172 | 2 |
| C71×#1546 | 2 |
| #10286 | 71 |