Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
458 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22597430 | C2 | semidirect |
| 3. #22588173 | C2 | semidirect |
| 6. #22586238 | C2 | semidirect |
| 7. C71×#1285 | C2 | semidirect |
| 11. #17986295 | C4 | semidirect |
| 12. #17986295 | C4 | semidirect |
| 13. #17986200 | C4 | semidirect |
| 14. #17986200 | C4 | semidirect |
| 210. #1285 | D71 | semidirect |
| 211. C71 | #9164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598463 | 2 |
| #22597430 | 2 |
| #22588173 | 2 |
| #22586952 | 2 |
| #22586834 | 2 |
| #22586238 | 2 |
| C71×#1285 | 2 |
| #9164 | 71 |