Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
324 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 324 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 |
|---|---|---|
| 3. C2×#17985774 | C2 | semidirect |
| 5. #22589086 | C2 | semidirect |
| 6. #22586437 | C2 | semidirect |
| 7. C71×#1381 | C2 | semidirect |
| 16. #17985804 | C4 | semidirect |
| 17. #17985801 | C4 | semidirect |
| 144. #1381 | D71 | semidirect |
| 145. C71 | #13152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985805 | 2 |
| #22590048 | 2 |
| C2×#17985774 | 2 |
| #22589226 | 2 |
| #22589086 | 2 |
| #22586437 | 2 |
| C71×#1381 | 2 |
| #13152 | 71 |