Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
728 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22589318 | C2 | semidirect |
| 3. #22589316 | C2 | semidirect |
| 5. #22587077 | C2 | semidirect |
| 7. C71×#1561 | C2 | semidirect |
| 8. #17986753 | C4 | semidirect |
| 231. #1561 | D71 | semidirect |
| 233. C71 | #8531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22602751 | 2 |
| #22589318 | 2 |
| #22589316 | 2 |
| #22589167 | 2 |
| #22587077 | 2 |
| #22587073 | 2 |
| C71×#1561 | 2 |
| #8531 | 71 |