Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
338 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22588481 | C2 | semidirect |
| 3. #22587108 | C2 | semidirect |
| 6. #22586231 | C2 | semidirect |
| 7. C71×#1302 | C2 | semidirect |
| 171. #1302 | D71 | semidirect |
| 173. C71 | #8917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597512 | 2 |
| #22588481 | 2 |
| #22587108 | 2 |
| #22586926 | 2 |
| #22586806 | 2 |
| #22586231 | 2 |
| C71×#1302 | 2 |
| #8917 | 71 |