Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
564 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22599278 | C2 | semidirect |
| 3. #22598688 | C2 | semidirect |
| 4. #22589163 | C2 | semidirect |
| 5. #22586899 | C2 | semidirect |
| 6. #22586184 | C2 | semidirect |
| 7. C71×#1518 | C2 | semidirect |
| 201. #1518 | D71 | semidirect |
| 204. C71 | #10219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599278 | 2 |
| #22599260 | 2 |
| #22598688 | 2 |
| #22589163 | 2 |
| #22586899 | 2 |
| #22586184 | 2 |
| C71×#1518 | 2 |
| #10219 | 71 |