Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
338 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #22588240 | C2 | semidirect |
| 5. #22586450 | C2 | semidirect |
| 6. #22586419 | C2 | semidirect |
| 7. C2×#365×C71 | C2 | semidirect |
| 16. #17985804 | C4 | semidirect |
| 17. #17985801 | C4 | semidirect |
| 149. C2×#365 | D71 | semidirect |
| 156. C71 | #13143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985808 | 2 |
| #22590053 | 2 |
| #22589231 | 2 |
| #22588240 | 2 |
| #22586450 | 2 |
| #22586419 | 2 |
| C2×#365×C71 | 2 |
| #13143 | 71 |