Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
406 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #22589086 | C2 | semidirect |
| 5. #22586441 | C2 | semidirect |
| 6. #22586421 | C2 | semidirect |
| 7. C71×#2155 | C2 | semidirect |
| 20. #17985810 | C4 | semidirect |
| 46. #14556060 | C2×C4 | semidirect |
| 56. M32×C71 | C2×C4 | semidirect |
| 156. #2155 | D71 | semidirect |
| 162. C71 | #12951 | semidirect |
| 203. M32 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597111 | 2 |
| #22590087 | 2 |
| #22590077 | 2 |
| #22589086 | 2 |
| #22586441 | 2 |
| #22586421 | 2 |
| C71×#2155 | 2 |
| #12951 | 71 |