Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
210 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 85. C71⋊C8 | Q32 | semidirect |
| 107. C71 | #12072 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Dic568 | 2 |
| #22587236 | 2 |
| #22587146 | 2 |
| #22586303 | 2 |
| #22586259 | 2 |
| C71×#1371 | 2 |
| #12072 | 71 |