Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
424 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #22597320 | C2 | semidirect |
| 3. #22586915 | C2 | semidirect |
| 4. #22586757 | C2 | semidirect |
| 5. #22586204 | C2 | semidirect |
| 6. #22586203 | C2 | semidirect |
| 7. C71×#1514 | C2 | semidirect |
| 9. #17986391 | C4 | semidirect |
| 10. #17986386 | C4 | semidirect |
| 11. #17986367 | C4 | semidirect |
| 12. #17986363 | C4 | semidirect |
| 208. #1514 | D71 | semidirect |
| 212. C71 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599377 | 2 |
| #22597320 | 2 |
| #22586915 | 2 |
| #22586757 | 2 |
| #22586204 | 2 |
| #22586203 | 2 |
| C71×#1514 | 2 |
| #9370 | 71 |