Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
348 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 67 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. #22590009 | C2 | semidirect |
| 3. #22586510 | C2 | semidirect |
| 4. #22586502 | C2 | semidirect |
| 5. C71×#2128 | C2 | semidirect |
| 6. #17986604 | C4 | semidirect |
| 7. #17986389 | C4 | semidirect |
| 10. #17986353 | C4 | semidirect |
| 15. #17986060 | C4 | semidirect |
| 27. #14556125 | C2×C4 | semidirect |
| 28. #14556120 | C2×C4 | semidirect |
| 42. #14556039 | C2×C4 | semidirect |
| 43. C4×C71⋊C8 | C2×C4 | semidirect |
| 161. #2128 | D71 | semidirect |
| 165. C71 | #13609 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22599390 | 2 |
| #22590009 | 2 |
| #22586510 | 2 |
| #22586502 | 2 |
| C71×#2128 | 2 |
| #13609 | 71 |