Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
384 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 105 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×#17985821 | C2 | semidirect |
| 5. #22586451 | C2 | semidirect |
| 6. #22586426 | C2 | semidirect |
| 7. C71×#1951 | C2 | semidirect |
| 17. #17985814 | C4 | semidirect |
| 18. #17985811 | C4 | semidirect |
| 149. #1951 | D71 | semidirect |
| 152. C71 | #12952 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597258 | 2 |
| C2×#17985821 | 2 |
| #22590087 | 2 |
| C2×#17985808 | 2 |
| #22586451 | 2 |
| #22586426 | 2 |
| C71×#1951 | 2 |
| #12952 | 71 |