Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
362 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 3. #22586452 | C2 | semidirect |
| 4. #22586434 | C2 | semidirect |
| 103. C71 | #12878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596951 | 2 |
| #22588390 | 2 |
| #22586452 | 2 |
| #22586434 | 2 |
| C71×#2113 | 2 |
| #12878 | 71 |