Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1004 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22602754 | C2 | semidirect |
| 2. #22599283 | C2 | semidirect |
| 4. #22587419 | C2 | semidirect |
| 5. #22587400 | C2 | semidirect |
| 6. #22586760 | C2 | semidirect |
| 7. C71×#1543 | C2 | semidirect |
| 10. #17986735 | C22 | semidirect |
| 11. #17986729 | C22 | semidirect |
| 26. #17985729 | C22 | semidirect |
| 29. #333×C71 | C22 | semidirect |
| 30. #331×C71 | C22 | semidirect |
| 173. #1543 | D71 | semidirect |
| 175. C71 | #18718 | semidirect |
| 196. #333 | C2×D71 | semidirect |
| 197. #331 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602754 | 2 |
| #22599283 | 2 |
| #22598793 | 2 |
| #22587419 | 2 |
| #22587400 | 2 |
| #22586760 | 2 |
| C71×#1543 | 2 |
| #18718 | 71 |