Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
180 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 51 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×#17985839 | C2 | semidirect |
| 5. #22586543 | C2 | semidirect |
| 6. #22586534 | C2 | semidirect |
| 7. C71×#1420 | C2 | semidirect |
| 96. #1420 | D71 | semidirect |
| 97. C71 | #13701 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985839 | 2 |
| #22590635 | 2 |
| #22590466 | 2 |
| #22590462 | 2 |
| #22586543 | 2 |
| #22586534 | 2 |
| C71×#1420 | 2 |
| #13701 | 71 |