Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
488 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22586761 | C2 | semidirect |
| 6. #22586230 | C2 | semidirect |
| 7. C71×#3139 | C2 | semidirect |
| 180. #3139 | D71 | semidirect |
| 185. C71 | #10114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599723 | 2 |
| #22599265 | 2 |
| #22589330 | 2 |
| #22586931 | 2 |
| #22586761 | 2 |
| #22586230 | 2 |
| C71×#3139 | 2 |
| #10114 | 71 |