Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 156. C71 | #10517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599682 | 2 |
| #22588460 | 2 |
| #22587041 | 2 |
| #22587040 | 2 |
| #22586851 | 2 |
| #22586209 | 2 |
| C71×#1506 | 2 |
| #10517 | 71 |