Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
554 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 554 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. #22589285 | C2 | semidirect |
| 5. #22586839 | C2 | semidirect |
| 6. #22586190 | C2 | semidirect |
| 7. C71×#3249 | C2 | semidirect |
| 196. #3249 | D71 | semidirect |
| 203. C71 | #10195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599278 | 2 |
| #22598716 | 2 |
| #22589285 | 2 |
| #22589266 | 2 |
| #22586839 | 2 |
| #22586190 | 2 |
| C71×#3249 | 2 |
| #10195 | 71 |