Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
430 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 430 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 |
|---|---|---|
| 188. C71 | #10217 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599731 | 2 |
| #22599556 | 2 |
| #22599554 | 2 |
| #22589321 | 2 |
| #22586851 | 2 |
| #22586250 | 2 |
| C71×#1506 | 2 |
| #10217 | 71 |