Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
3550 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 627 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 |
|---|---|---|
| 1. #22596592 | C2 | direct (N × H) |
| 2. C2×#17985912 | C2 | semidirect |
| 3. C2×#17985911 | C2 | semidirect |
| 4. C2×#17985910 | C2 | semidirect |
| 6. C2×#393×C71 | C2 | semidirect |
| 8. C23×Dic142 | C22 | semidirect |
| 12. #17985912 | C22 | semidirect |
| 13. #17985911 | C22 | semidirect |
| 14. #17985910 | C22 | semidirect |
| 16. C2×C71⋊#95 | C22 | semidirect |
| 17. C2×C71⋊#95 | C22 | semidirect |
| 18. C23×Q8×C71 | C22 | semidirect |
| 20. #393×C71 | C22 | semidirect |
| 21. C2×#95×C71 | C22 | semidirect |
| 24. C24×D71 | Q8 | semidirect |
| 29. C22×Dic142 | C23 | semidirect |
| 37. C71⋊#95 | C23 | semidirect |
| 38. C71⋊#95 | C23 | semidirect |
| 41. C22×Q8×C71 | C23 | semidirect |
| 46. #95×C71 | C23 | semidirect |
| 55. C23×D71 | C2×Q8 | semidirect |
| 133. C2×C71 | #2840 | semidirect |
| 142. C2×#393 | D71 | semidirect |
| 144. C71 | C2×#2840 | semidirect |
| 147. C23×Q8 | C2×D71 | semidirect |
| 155. #393 | C2×D71 | semidirect |
| 159. C2×#95 | C2×D71 | semidirect |
| 170. C22×Q8 | C22×D71 | semidirect |
| 184. #95 | C22×D71 | semidirect |
| 271. C2 | #22596592 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22596592 | 2 |
| C2×#17985912 | 2 |
| C2×#17985911 | 2 |
| C2×#17985910 | 2 |
| C2×#17985854 | 2 |
| C2×#393×C71 | 2 |
| C2×#2840 | 71 |