Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
342 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 91 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. C2×C32×D71 | C2 | semidirect |
| 3. #366×D71 | C2 | semidirect |
| 4. #22586519 | C2 | semidirect |
| 5. #22586518 | C2 | semidirect |
| 6. #22586517 | C2 | semidirect |
| 7. C71×#1415 | C2 | semidirect |
| 12. D16×D71 | C4 | semidirect |
| 15. C2×C71⋊C32 | C22 | semidirect |
| 17. #17985825 | C22 | semidirect |
| 20. C2×C32×C71 | C22 | semidirect |
| 21. #366×C71 | C22 | semidirect |
| 30. D1136 | C2×C4 | semidirect |
| 40. D16×C71 | C2×C4 | semidirect |
| 110. D71 | #1415 | direct (N × H) |
| 117. #1415 | D71 | direct (N × H) |
| 118. C71 | C2×#1415 | semidirect |
| 129. C2×C32 | C2×D71 | semidirect |
| 132. #366 | C2×D71 | semidirect |
| 145. D16 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D71 | 2 |
| C2×C32×D71 | 2 |
| #366×D71 | 2 |
| #22586519 | 2 |
| #22586518 | 2 |
| #22586517 | 2 |
| C71×#1415 | 2 |
| C2×#1415 | 71 |