Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
364 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 2. #22588477 | C2 | semidirect |
| 4. #22586795 | C2 | semidirect |
| 6. C71⋊#1309 | C2 | semidirect |
| 7. C71×#1561 | C2 | semidirect |
| 166. #1561 | D71 | semidirect |
| 171. C71 | #10533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599723 | 2 |
| #22588477 | 2 |
| #22587073 | 2 |
| #22586795 | 2 |
| #22586790 | 2 |
| C71⋊#1309 | 2 |
| C71×#1561 | 2 |
| #10533 | 71 |