Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
478 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 4. C2×#17985736 | C2 | semidirect |
| 5. #22586227 | C2 | semidirect |
| 6. #22586182 | C2 | semidirect |
| 7. C71×#1472 | C2 | semidirect |
| 10. #17986329 | C4 | semidirect |
| 11. #17986312 | C4 | semidirect |
| 15. #17986155 | C4 | semidirect |
| 16. #17986138 | C4 | semidirect |
| 238. #1472 | D71 | semidirect |
| 241. C71 | #9263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599121 | 2 |
| #22597394 | 2 |
| #22586845 | 2 |
| C2×#17985736 | 2 |
| #22586227 | 2 |
| #22586182 | 2 |
| C71×#1472 | 2 |
| #9263 | 71 |