Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22589330 | C2 | semidirect |
| 5. C71⋊#1309 | C2 | semidirect |
| 6. #22586231 | C2 | semidirect |
| 7. C71×#1548 | C2 | semidirect |
| 189. #1548 | D71 | semidirect |
| 193. C71 | #9353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597823 | 2 |
| #22597461 | 2 |
| #22589330 | 2 |
| #22586777 | 2 |
| C71⋊#1309 | 2 |
| #22586231 | 2 |
| C71×#1548 | 2 |
| #9353 | 71 |