Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1258 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 259 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. #22589182 | C2 | semidirect |
| 120. C2×Dic71 | #101 | semidirect |
| 151. C71 | #21799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556126 | 2 |
| #22596969 | 2 |
| #22589182 | 2 |
| #22588264 | 2 |
| #22588263 | 2 |
| C71×#1784 | 2 |
| #21799 | 71 |