Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22588086 | C2 | semidirect |
| 3. #22586165 | C2 | semidirect |
| 5. C71×#1839 | C2 | semidirect |
| 167. #1839 | D71 | semidirect |
| 171. C71 | #7656 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596712 | 2 |
| #22588086 | 2 |
| #22586165 | 2 |
| #22586160 | 2 |
| C71×#1839 | 2 |
| #7656 | 71 |