Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
306 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 101 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. M64×D71 | C2 | semidirect |
| 3. #22586480 | C2 | semidirect |
| 4. #22586479 | C2 | semidirect |
| 5. C71×#1400 | C2 | semidirect |
| 14. #17985833 | C22 | semidirect |
| 18. M64×C71 | C22 | semidirect |
| 129. D71 | #1400 | direct (N × H) |
| 134. #1400 | D71 | direct (N × H) |
| 135. C71 | C2×#1400 | semidirect |
| 147. M64 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M32×D71 | 2 |
| M64×D71 | 2 |
| #22586480 | 2 |
| #22586479 | 2 |
| C71×#1400 | 2 |
| C2×#1400 | 71 |