Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
472 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 3. #22588427 | C2 | semidirect |
| 4. #22588418 | C2 | semidirect |
| 6. #22586247 | C2 | semidirect |
| 7. C71×#1293 | C2 | semidirect |
| 10. #17986335 | C4 | semidirect |
| 12. #17986318 | C4 | semidirect |
| 223. #1293 | D71 | semidirect |
| 224. C71 | #9522 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598265 | 2 |
| #22597385 | 2 |
| #22588427 | 2 |
| #22588418 | 2 |
| #22586884 | 2 |
| #22586247 | 2 |
| C71×#1293 | 2 |
| #9522 | 71 |