Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
972 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 972 conjugacy classes of subgroups — too many to draw. Only its 205 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. #430×D71 | C2 | semidirect |
| 3. #22589857 | C2 | semidirect |
| 4. #22589856 | C2 | semidirect |
| 5. #22589855 | C2 | semidirect |
| 6. #338×D71 | C2 | semidirect |
| 7. C71×#2091 | C2 | semidirect |
| 159. #2091 | D71 | semidirect |
| 161. C71 | #23723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #430×D71 | 2 |
| #22596783 | 2 |
| #22589857 | 2 |
| #22589856 | 2 |
| #22589855 | 2 |
| #338×D71 | 2 |
| C71×#2091 | 2 |
| #23723 | 71 |