Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
470 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. #22589330 | C2 | semidirect |
| 4. #22587098 | C2 | semidirect |
| 6. #22586630 | C2 | semidirect |
| 7. C71×#1549 | C2 | semidirect |
| 155. #1549 | D71 | semidirect |
| 158. C71 | #9812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986347 | 2 |
| #22589330 | 2 |
| #22589179 | 2 |
| #22587098 | 2 |
| #22587007 | 2 |
| #22586630 | 2 |
| C71×#1549 | 2 |
| #9812 | 71 |