Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
424 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22597327 | C2 | semidirect |
| 3. #22586886 | C2 | semidirect |
| 4. #22586756 | C2 | semidirect |
| 5. #22586204 | C2 | semidirect |
| 6. #22586202 | C2 | semidirect |
| 7. C71×#1521 | C2 | semidirect |
| 9. #17986394 | C4 | semidirect |
| 10. #17986389 | C4 | semidirect |
| 11. #17986369 | C4 | semidirect |
| 12. #17986365 | C4 | semidirect |
| 207. #1521 | D71 | semidirect |
| 212. C71 | #9370 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599373 | 2 |
| #22597327 | 2 |
| #22586886 | 2 |
| #22586756 | 2 |
| #22586204 | 2 |
| #22586202 | 2 |
| C71×#1521 | 2 |
| #9370 | 71 |