Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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. #22601442 | C2 | semidirect |
| 3. C2×#17985809 | C2 | semidirect |
| 4. #22588396 | C2 | semidirect |
| 5. #22586453 | C2 | semidirect |
| 6. #22586439 | C2 | semidirect |
| 7. C71×#2143 | C2 | semidirect |
| 14. #17986271 | C4 | semidirect |
| 15. #17986266 | C4 | semidirect |
| 182. #2143 | D71 | semidirect |
| 186. C71 | #13070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601442 | 2 |
| #22598056 | 2 |
| C2×#17985809 | 2 |
| #22588396 | 2 |
| #22586453 | 2 |
| #22586439 | 2 |
| C71×#2143 | 2 |
| #13070 | 71 |