Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
332 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22589088 | C2 | semidirect |
| 5. #22586436 | C2 | semidirect |
| 6. #22586434 | C2 | semidirect |
| 7. C2×C4×C16×C71 | C2 | semidirect |
| 16. #17985804 | C4 | semidirect |
| 17. #17985801 | C4 | semidirect |
| 140. C2×C4×C16 | D71 | semidirect |
| 145. C71 | #13151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985807 | 2 |
| #22590048 | 2 |
| #22589228 | 2 |
| #22589088 | 2 |
| #22586436 | 2 |
| #22586434 | 2 |
| C2×C4×C16×C71 | 2 |
| #13151 | 71 |