Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
392 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22589959 | C2 | semidirect |
| 3. #22588389 | C2 | semidirect |
| 4. #22586332 | C2 | semidirect |
| 5. #22586331 | C2 | semidirect |
| 6. #22586330 | C2 | semidirect |
| 7. C71×#1341 | C2 | semidirect |
| 21. #17985781 | C22 | semidirect |
| 23. C71⋊#338 | C22 | semidirect |
| 25. #349×C71 | C22 | semidirect |
| 26. #338×C71 | C22 | semidirect |
| 195. #1341 | D71 | semidirect |
| 196. C71 | #11870 | semidirect |
| 213. #349 | C2×D71 | semidirect |
| 215. #338 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597986 | 2 |
| #22589959 | 2 |
| #22588389 | 2 |
| #22586332 | 2 |
| #22586331 | 2 |
| #22586330 | 2 |
| C71×#1341 | 2 |
| #11870 | 71 |