Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
172 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 59 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. #22586416 | C2 | semidirect |
| 4. #22586401 | C2 | semidirect |
| 5. C71×#2253 | C2 | semidirect |
| 71. #2253 | D71 | semidirect |
| 76. C71 | #12464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590513 | 2 |
| #22590178 | 2 |
| #22586416 | 2 |
| #22586401 | 2 |
| C71×#2253 | 2 |
| #12464 | 71 |