Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
292 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22586456 | C2 | semidirect |
| 5. #22586451 | C2 | semidirect |
| 6. #22586426 | C2 | semidirect |
| 7. C71×#1833 | C2 | semidirect |
| 132. #1833 | D71 | semidirect |
| 136. C71 | #13490 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17985811 | 2 |
| #22590055 | 2 |
| #22589250 | 2 |
| #22586456 | 2 |
| #22586451 | 2 |
| #22586426 | 2 |
| C71×#1833 | 2 |
| #13490 | 71 |