Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
384 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 97 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. C4×#14556059 | C2 | semidirect |
| 3. #22587101 | C2 | semidirect |
| 6. #22586197 | C2 | semidirect |
| 7. C71×#1285 | C2 | semidirect |
| 9. #17986126 | C4 | semidirect |
| 10. #17986123 | C4 | semidirect |
| 11. #17986076 | C4 | semidirect |
| 13. #17986064 | C4 | semidirect |
| 185. #1285 | D71 | semidirect |
| 186. C71 | #8696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22597309 | 2 |
| C4×#14556059 | 2 |
| #22587101 | 2 |
| #22586866 | 2 |
| #22586863 | 2 |
| #22586197 | 2 |
| C71×#1285 | 2 |
| #8696 | 71 |