Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
204 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. C2×C32×D71 | C2 | semidirect |
| 2. #22590428 | C2 | semidirect |
| 4. #22586542 | C2 | semidirect |
| 5. #22586521 | C2 | semidirect |
| 6. #22586518 | C2 | semidirect |
| 7. C2×SD64×C71 | C2 | semidirect |
| 39. C32×C71 | D4 | semidirect |
| 83. C2×D71 | SD64 | semidirect |
| 96. C2×SD64 | D71 | semidirect |
| 103. C71 | #13696 | semidirect |
| 135. C32 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×D71 | 2 |
| #22590428 | 2 |
| #22590423 | 2 |
| #22586542 | 2 |
| #22586521 | 2 |
| #22586518 | 2 |
| C2×SD64×C71 | 2 |
| #13696 | 71 |