Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
712 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×#17986436 | C2 | semidirect |
| 2. #22600024 | C2 | semidirect |
| 3. #22590450 | C2 | semidirect |
| 4. #22590392 | C2 | semidirect |
| 5. #22590279 | C2 | semidirect |
| 6. #22590250 | C2 | semidirect |
| 7. C4×D1136 | C2 | semidirect |
| 8. #22590173 | C2 | semidirect |
| 9. C71×#2249 | C2 | semidirect |
| 11. C2×D8×D71 | C22 | semidirect |
| 14. C2×#14556071 | C22 | semidirect |
| 17. C2×#14556067 | C22 | semidirect |
| 18. #17986237 | C22 | semidirect |
| 23. C4×D568 | C22 | semidirect |
| 25. #17985825 | C22 | semidirect |
| 26. C4⋊(C71⋊C16) | C22 | semidirect |
| 27. #17985803 | C22 | semidirect |
| 28. #17985801 | C22 | semidirect |
| 29. #17985800 | C22 | semidirect |
| 30. (C2×D71)⋊C16 | C22 | semidirect |
| 31. C2×Q32×C71 | C22 | semidirect |
| 32. C2×SD32×C71 | C22 | semidirect |
| 34. #495×C71 | C22 | semidirect |
| 35. C4×C16×C71 | C22 | semidirect |
| 55. D1136 | D4 | semidirect |
| 174. #2249 | D71 | semidirect |
| 181. C71 | #33839 | semidirect |
| 186. C2×Q32 | C2×D71 | semidirect |
| 188. C2×SD32 | C2×D71 | semidirect |
| 193. #495 | C2×D71 | semidirect |
| 207. C4×C16 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986436 | 2 |
| #22600024 | 2 |
| #22590450 | 2 |
| #22590392 | 2 |
| #22590279 | 2 |
| #22590250 | 2 |
| C4×D1136 | 2 |
| #22590173 | 2 |
| C71×#2249 | 2 |
| #33839 | 71 |