Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
250 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 67 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×#17985838 | C2 | semidirect |
| 2. C2×#17985837 | C2 | semidirect |
| 3. C2×#17985836 | C2 | semidirect |
| 4. #22590591 | C2 | semidirect |
| 6. C32×Dic71 | C2 | semidirect |
| 7. C2×SD64×C71 | C2 | semidirect |
| 37. C71⋊C32 | D4 | semidirect |
| 45. C32×C71 | D4 | semidirect |
| 95. Dic71 | SD64 | semidirect |
| 104. C2×SD64 | D71 | semidirect |
| 108. C71 | #13727 | semidirect |
| 146. C32 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985838 | 2 |
| C2×#17985837 | 2 |
| C2×#17985836 | 2 |
| #22590591 | 2 |
| #22590588 | 2 |
| C32×Dic71 | 2 |
| C2×SD64×C71 | 2 |
| #13727 | 71 |