Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
676 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22589322 | C2 | semidirect |
| 3. #22587071 | C2 | semidirect |
| 5. #22586853 | C2 | semidirect |
| 7. C71×#1537 | C2 | semidirect |
| 11. #17986723 | C4 | semidirect |
| 14. #17986664 | C4 | semidirect |
| 211. #1537 | D71 | semidirect |
| 214. C71 | #8496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602751 | 2 |
| #22589322 | 2 |
| #22587071 | 2 |
| #22587063 | 2 |
| #22586853 | 2 |
| #22586849 | 2 |
| C71×#1537 | 2 |
| #8496 | 71 |