Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
200 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22586539 | C2 | semidirect |
| 4. #22586521 | C2 | semidirect |
| 6. #22586474 | C2 | semidirect |
| 7. C4×Q32×C71 | C2 | semidirect |
| 10. #17985836 | C4 | semidirect |
| 27. C71⋊C32 | C2×C4 | semidirect |
| 31. Q32×C71 | C2×C4 | semidirect |
| 87. C4×Q32 | D71 | semidirect |
| 93. C71 | #13652 | semidirect |
| 111. Q32 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985836 | 2 |
| C4×D1136 | 2 |
| #22586539 | 2 |
| #22586521 | 2 |
| #22586517 | 2 |
| #22586474 | 2 |
| C4×Q32×C71 | 2 |
| #13652 | 71 |