Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
536 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 1. #22599335 | C2 | semidirect |
| 2. #22589171 | C2 | semidirect |
| 3. #22586848 | C2 | semidirect |
| 4. #22586251 | C2 | semidirect |
| 5. C71×#3253 | C2 | semidirect |
| 137. #3253 | D71 | semidirect |
| 142. C71 | #10212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599335 | 2 |
| #22589171 | 2 |
| #22586848 | 2 |
| #22586251 | 2 |
| C71×#3253 | 2 |
| #10212 | 71 |