Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
512 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 101 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. #22589293 | C2 | semidirect |
| 5. #22586839 | C2 | semidirect |
| 6. #22586191 | C2 | semidirect |
| 7. C71×#3139 | C2 | semidirect |
| 192. #3139 | D71 | semidirect |
| 197. C71 | #10205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599652 | 2 |
| #22599461 | 2 |
| #22589293 | 2 |
| #22589259 | 2 |
| #22586839 | 2 |
| #22586191 | 2 |
| C71×#3139 | 2 |
| #10205 | 71 |