Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
446 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22589179 | C2 | semidirect |
| 3. #22587073 | C2 | semidirect |
| 4. #22587007 | C2 | semidirect |
| 5. #22586756 | C2 | semidirect |
| 6. #22586231 | C2 | semidirect |
| 7. C71×#1574 | C2 | semidirect |
| 175. #1574 | D71 | semidirect |
| 180. C71 | #10488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599260 | 2 |
| #22589179 | 2 |
| #22587073 | 2 |
| #22587007 | 2 |
| #22586756 | 2 |
| #22586231 | 2 |
| C71×#1574 | 2 |
| #10488 | 71 |