Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
346 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 9. #17986403 | C4 | semidirect |
| 10. #17986377 | C4 | semidirect |
| 14. Q16×Dic71 | C4 | semidirect |
| 15. #17986093 | C4 | semidirect |
| 164. C71 | #11745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598921 | 2 |
| #22590140 | 2 |
| #22588228 | 2 |
| #22586353 | 2 |
| #22586352 | 2 |
| #22586351 | 2 |
| C71×#1348 | 2 |
| #11745 | 71 |