Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
496 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 496 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 |
|---|---|---|
| 2. C2×#17985781 | C2 | semidirect |
| 3. #22586324 | C2 | direct (N × H) |
| 4. C2×H(3,ℤ/4)×C71 | C2 | semidirect |
| 5. C22×D568 | C4 | semidirect |
| 10. #17986252 | C4 | semidirect |
| 12. C2×#14556060 | C4 | semidirect |
| 15. #17985781 | C22 | semidirect |
| 19. H(3,ℤ/4)×C71 | C22 | semidirect |
| 25. C2×D568 | C2×C4 | semidirect |
| 36. #14556060 | C2×C4 | semidirect |
| 174. C2×C71 | #1339 | semidirect |
| 179. C2×H(3,ℤ/4) | D71 | semidirect |
| 181. C71 | C2×#1339 | semidirect |
| 196. H(3,ℤ/4) | C2×D71 | semidirect |
| 351. C2 | #22586324 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986252 | 2 |
| C2×#17985781 | 2 |
| #22586324 | 2 |
| C2×H(3,ℤ/4)×C71 | 2 |
| C2×#1339 | 71 |