Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
374 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 177. C71 | #10462 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598141 | 2 |
| #22588333 | 2 |
| #22587095 | 2 |
| #22586795 | 2 |
| C2×#17985729 | 2 |
| #22586215 | 2 |
| C71×#1550 | 2 |
| #10462 | 71 |