Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
512 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22587066 | C2 | semidirect |
| 5. #22586852 | C2 | semidirect |
| 6. #22586234 | C2 | semidirect |
| 7. C71×#3139 | C2 | semidirect |
| 181. #3139 | D71 | semidirect |
| 187. C71 | #10098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599339 | 2 |
| #22594281 | 2 |
| #22587066 | 2 |
| #22586937 | 2 |
| #22586852 | 2 |
| #22586234 | 2 |
| C71×#3139 | 2 |
| #10098 | 71 |