Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22590198 | C2 | semidirect |
| 4. #22586520 | C2 | semidirect |
| 6. #22586473 | C2 | semidirect |
| 7. C71×#1423 | C2 | semidirect |
| 12. #17985838 | C4 | semidirect |
| 25. Dic568 | C2×C4 | semidirect |
| 36. C32×C71 | C2×C4 | semidirect |
| 89. #1423 | D71 | semidirect |
| 93. C71 | #13652 | semidirect |
| 122. C32 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985838 | 2 |
| #22590198 | 2 |
| #22590186 | 2 |
| #22586520 | 2 |
| #22586517 | 2 |
| #22586473 | 2 |
| C71×#1423 | 2 |
| #13652 | 71 |