Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
994 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 167 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. #22599077 | C2 | semidirect |
| 2. #22599076 | C2 | semidirect |
| 3. #22598791 | C2 | semidirect |
| 4. #22598787 | C2 | semidirect |
| 5. #22588005 | C2 | semidirect |
| 6. #22587970 | C2 | semidirect |
| 7. #22587968 | C2 | semidirect |
| 8. #22587954 | C2 | semidirect |
| 9. #22587926 | C2 | semidirect |
| 10. #22586644 | C2 | semidirect |
| 11. C71×#1721 | C2 | semidirect |
| 17. #17986397 | C22 | semidirect |
| 18. #17986395 | C22 | semidirect |
| 24. #17986375 | C22 | semidirect |
| 28. #17986346 | C22 | semidirect |
| 29. #17986345 | C22 | semidirect |
| 36. #17985721 | C22 | semidirect |
| 37. C8×C71⋊C8 | C22 | semidirect |
| 39. #493×C71 | C22 | semidirect |
| 41. #486×C71 | C22 | semidirect |
| 42. #322×C71 | C22 | semidirect |
| 171. C8×C71 | AGL(1,ℤ/8) | semidirect |
| 173. C71⋊C8 | AGL(1,ℤ/8) | semidirect |
| 206. #1721 | D71 | semidirect |
| 212. C71 | #19745 | semidirect |
| 227. #493 | C2×D71 | semidirect |
| 234. #486 | C2×D71 | semidirect |
| 242. #322 | C2×D71 | semidirect |
| 374. C8 | #14556152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599077 | 2 |
| #22599076 | 2 |
| #22598791 | 2 |
| #22598787 | 2 |
| #22588005 | 2 |
| #22587970 | 2 |
| #22587968 | 2 |
| #22587954 | 2 |
| #22587926 | 2 |
| #22586644 | 2 |
| C71×#1721 | 2 |
| #19745 | 71 |