Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
212 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22587248 | C2 | semidirect |
| 4. #22586405 | C2 | semidirect |
| 5. #22586311 | C2 | semidirect |
| 6. #22586262 | C2 | semidirect |
| 55. C71⋊C16 | M16 | semidirect |
| 110. C71 | #12087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590204 | 2 |
| #22587254 | 2 |
| #22587248 | 2 |
| #22586405 | 2 |
| #22586311 | 2 |
| #22586262 | 2 |
| C71×#1333 | 2 |
| #12087 | 71 |