Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
436 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 196. C71 | #9190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597424 | 2 |
| #22594217 | 2 |
| C4×#14556046 | 2 |
| #22586942 | 2 |
| #22586206 | 2 |
| #22586205 | 2 |
| C71×#1528 | 2 |
| #9190 | 71 |