Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22591086 | C2 | semidirect |
| 4. #22587020 | C2 | semidirect |
| 5. #22586198 | C2 | semidirect |
| 6. #22586168 | C2 | semidirect |
| 9. #17986371 | C4 | semidirect |
| 10. #17986351 | C4 | semidirect |
| 87. C4×Dic71 | SD16 | semidirect |
| 190. C71 | #9301 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599262 | 2 |
| #22591086 | 2 |
| #22589173 | 2 |
| #22587020 | 2 |
| #22586198 | 2 |
| #22586168 | 2 |
| C71×#1517 | 2 |
| #9301 | 71 |