Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
494 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 143 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×#17985776 | C2 | semidirect |
| 4. #22586422 | C2 | semidirect |
| 5. C71×#1376 | C2 | semidirect |
| 14. #17985780 | C4 | semidirect |
| 34. #14556068 | C2×C4 | semidirect |
| 43. M32×C71 | C2×C4 | semidirect |
| 135. #1376 | D71 | semidirect |
| 136. C71 | #12607 | semidirect |
| 170. M32 | C4×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11765848 | 2 |
| C2×#17985780 | 2 |
| C2×#17985776 | 2 |
| #22586422 | 2 |
| C71×#1376 | 2 |
| #12607 | 71 |