Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 135. C71 | #12413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601309 | 2 |
| #22590623 | 2 |
| #22590479 | 2 |
| #22586393 | 2 |
| #22586322 | 2 |
| #22586309 | 2 |
| C71×#1696 | 2 |
| #12413 | 71 |