Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
530 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. #22591155 | C2 | semidirect |
| 3. #22589259 | C2 | semidirect |
| 4. #22586888 | C2 | semidirect |
| 5. #22586205 | C2 | semidirect |
| 6. #22586197 | C2 | semidirect |
| 7. C71×#1527 | C2 | semidirect |
| 9. #17986389 | C4 | semidirect |
| 10. #17986358 | C4 | semidirect |
| 35. #14556128 | C2×C4 | semidirect |
| 36. #14556125 | C2×C4 | semidirect |
| 56. #14556039 | C2×C4 | semidirect |
| 225. #1527 | D71 | semidirect |
| 229. C71 | #9381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599327 | 2 |
| #22591155 | 2 |
| #22589259 | 2 |
| #22586888 | 2 |
| #22586205 | 2 |
| #22586197 | 2 |
| C71×#1527 | 2 |
| #9381 | 71 |