Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
256 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22587933 | C2 | semidirect |
| 3. D8×C71⋊C8 | C2 | semidirect |
| 4. #22586403 | C2 | semidirect |
| 5. #22586395 | C2 | semidirect |
| 6. #22586387 | C2 | semidirect |
| 7. C71×#2224 | C2 | semidirect |
| 63. D8×C71 | SD16 | semidirect |
| 96. C71⋊C8 | D16 | semidirect |
| 117. #2224 | D71 | semidirect |
| 124. C71 | #12416 | semidirect |
| 174. D8 | #11765852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22590375 | 2 |
| #22587933 | 2 |
| D8×C71⋊C8 | 2 |
| #22586403 | 2 |
| #22586395 | 2 |
| #22586387 | 2 |
| C71×#2224 | 2 |
| #12416 | 71 |