Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1126 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1126 conjugacy classes of subgroups — too many to draw. Only its 219 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. C2×#17986729 | C2 | semidirect |
| 4. #22587419 | C2 | direct (N × H) |
| 5. C2×#17985729 | C2 | semidirect |
| 6. C2×#333×C71 | C2 | semidirect |
| 11. #17986729 | C22 | semidirect |
| 23. #17985729 | C22 | semidirect |
| 26. #333×C71 | C22 | semidirect |
| 71. C2×Dic142 | SD16 | semidirect |
| 134. Dic142 | C2×SD16 | semidirect |
| 152. C2×C71 | #1623 | semidirect |
| 160. C2×#333 | D71 | semidirect |
| 162. C71 | C2×#1623 | semidirect |
| 181. #333 | C2×D71 | semidirect |
| 308. C2 | #22587419 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986729 | 2 |
| C2×#17986373 | 2 |
| C2×#17986200 | 2 |
| #22587419 | 2 |
| C2×#17985729 | 2 |
| C2×#333×C71 | 2 |
| C2×#1623 | 71 |