Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
598 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. #22598372 | C2 | semidirect |
| 3. #22591626 | C2 | semidirect |
| 4. #22589172 | C2 | semidirect |
| 5. #22586770 | C2 | semidirect |
| 6. #22586766 | C2 | semidirect |
| 7. C71×#1274 | C2 | semidirect |
| 223. #1274 | D71 | semidirect |
| 224. C71 | #10013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598372 | 2 |
| #22598341 | 2 |
| #22591626 | 2 |
| #22589172 | 2 |
| #22586770 | 2 |
| #22586766 | 2 |
| C71×#1274 | 2 |
| #10013 | 71 |