Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
406 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 406 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. #22590114 | C2 | semidirect |
| 5. #22586441 | C2 | semidirect |
| 6. #22586422 | C2 | semidirect |
| 7. C71×#1945 | C2 | semidirect |
| 20. #17985808 | C4 | semidirect |
| 43. #14556068 | C2×C4 | semidirect |
| 58. #106×C71 | C2×C4 | semidirect |
| 159. #1945 | D71 | semidirect |
| 162. C71 | #12951 | semidirect |
| 211. #106 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14556150 | 2 |
| #22590114 | 2 |
| #22590087 | 2 |
| #22590075 | 2 |
| #22586441 | 2 |
| #22586422 | 2 |
| C71×#1945 | 2 |
| #12951 | 71 |