Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
392 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22587125 | C2 | semidirect |
| 4. #22587041 | C2 | semidirect |
| 5. #22586840 | C2 | semidirect |
| 6. #22586195 | C2 | semidirect |
| 191. C71 | #10510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599343 | 2 |
| #22589273 | 2 |
| #22587125 | 2 |
| #22587041 | 2 |
| #22586840 | 2 |
| #22586195 | 2 |
| C71×#1469 | 2 |
| #10510 | 71 |