Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
234 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22590590 | C2 | semidirect |
| 2. #22590416 | C2 | semidirect |
| 3. #22586416 | C2 | semidirect |
| 4. #22586376 | C2 | semidirect |
| 5. C71×#2170 | C2 | semidirect |
| 87. #2170 | D71 | semidirect |
| 90. C71 | #12436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590590 | 2 |
| #22590416 | 2 |
| #22586416 | 2 |
| #22586376 | 2 |
| C71×#2170 | 2 |
| #12436 | 71 |