Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
212 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22587250 | C2 | semidirect |
| 4. #22586406 | C2 | semidirect |
| 5. #22586311 | C2 | semidirect |
| 7. C71×#1313 | C2 | semidirect |
| 66. C16×C71 | M16 | semidirect |
| 109. #1313 | D71 | semidirect |
| 110. C71 | #12087 | semidirect |
| 169. C16 | #11765848 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590206 | 2 |
| #22587255 | 2 |
| #22587250 | 2 |
| #22586406 | 2 |
| #22586311 | 2 |
| #22586308 | 2 |
| C71×#1313 | 2 |
| #12087 | 71 |