Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
766 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 111 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. #22589138 | C2 | semidirect |
| 3. #22587041 | C2 | semidirect |
| 4. #22587035 | C2 | semidirect |
| 5. #22586954 | C2 | semidirect |
| 6. #22586680 | C2 | semidirect |
| 7. C71×#1530 | C2 | semidirect |
| 228. #1530 | D71 | semidirect |
| 230. C71 | #8458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602189 | 2 |
| #22589138 | 2 |
| #22587041 | 2 |
| #22587035 | 2 |
| #22586954 | 2 |
| #22586680 | 2 |
| C71×#1530 | 2 |
| #8458 | 71 |