Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
512 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22599000 | C2 | semidirect |
| 3. #22590561 | C2 | semidirect |
| 4. #22590513 | C2 | semidirect |
| 5. #22590422 | C2 | semidirect |
| 6. #22590421 | C2 | semidirect |
| 8. #22590230 | C2 | semidirect |
| 9. #22590228 | C2 | semidirect |
| 10. #22590155 | C2 | semidirect |
| 11. C71×#2231 | C2 | semidirect |
| 17. #17986379 | C22 | semidirect |
| 26. #17986105 | C22 | semidirect |
| 31. #17985821 | C22 | semidirect |
| 32. #17985820 | C22 | semidirect |
| 33. #17985816 | C22 | semidirect |
| 34. #17985814 | C22 | semidirect |
| 37. #17985776 | C22 | semidirect |
| 38. #499×C71 | C22 | semidirect |
| 40. #365×C71 | C22 | semidirect |
| 41. #364×C71 | C22 | semidirect |
| 211. #2231 | D71 | semidirect |
| 218. C71 | #33693 | semidirect |
| 224. #499 | C2×D71 | semidirect |
| 241. #365 | C2×D71 | semidirect |
| 243. #364 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599000 | 2 |
| #22597238 | 2 |
| #22590561 | 2 |
| #22590513 | 2 |
| #22590422 | 2 |
| #22590421 | 2 |
| #22590292 | 2 |
| #22590230 | 2 |
| #22590228 | 2 |
| #22590155 | 2 |
| C71×#2231 | 2 |
| #33693 | 71 |