Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22586403 | C2 | semidirect |
| 4. Q8⋊(C71⋊C16) | C2 | semidirect |
| 6. C16×C71⋊C8 | C2 | semidirect |
| 7. C71×#2183 | C2 | semidirect |
| 67. C16×C71 | SD16 | semidirect |
| 88. C71⋊C8 | M32 | semidirect |
| 106. #2183 | D71 | semidirect |
| 113. C71 | #12051 | semidirect |
| 173. C16 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590173 | 2 |
| C8×#11765852 | 2 |
| #22586403 | 2 |
| Q8⋊(C71⋊C16) | 2 |
| #22586294 | 2 |
| C16×C71⋊C8 | 2 |
| C71×#2183 | 2 |
| #12051 | 71 |