Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
650 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22599260 | C2 | semidirect |
| 2. #22599255 | C2 | semidirect |
| 3. #22598785 | C2 | semidirect |
| 4. #22589163 | C2 | semidirect |
| 5. #22586899 | C2 | semidirect |
| 6. #22586184 | C2 | semidirect |
| 7. C71×#1517 | C2 | semidirect |
| 106. C2×C71⋊C8 | D8 | semidirect |
| 218. #1517 | D71 | semidirect |
| 220. C71 | #10218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599260 | 2 |
| #22599255 | 2 |
| #22598785 | 2 |
| #22589163 | 2 |
| #22586899 | 2 |
| #22586184 | 2 |
| C71×#1517 | 2 |
| #10218 | 71 |