Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
312 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22589939 | C2 | semidirect |
| 5. #22589128 | C2 | semidirect |
| 6. #22586435 | C2 | semidirect |
| 7. C71×#1389 | C2 | semidirect |
| 15. #17985816 | C4 | semidirect |
| 16. #17985813 | C4 | semidirect |
| 146. #1389 | D71 | semidirect |
| 148. C71 | #13146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590090 | 2 |
| C2×#17985805 | 2 |
| #22589939 | 2 |
| #22589236 | 2 |
| #22589128 | 2 |
| #22586435 | 2 |
| C71×#1389 | 2 |
| #13146 | 71 |