Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
812 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 151 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×D16×D71 | C2 | semidirect |
| 2. #22600015 | C2 | semidirect |
| 3. #22590423 | C2 | semidirect |
| 4. #22590372 | C2 | semidirect |
| 5. #22590250 | C2 | semidirect |
| 6. C4×D1136 | C2 | semidirect |
| 7. C16×D284 | C2 | semidirect |
| 8. C71×#2246 | C2 | semidirect |
| 9. C2×D8×D71 | C22 | semidirect |
| 12. C2×#14556069 | C22 | semidirect |
| 14. C2×C16×D71 | C22 | semidirect |
| 15. #17986232 | C22 | semidirect |
| 18. C4×D568 | C22 | semidirect |
| 20. #17985825 | C22 | semidirect |
| 21. C4⋊(C71⋊C16) | C22 | semidirect |
| 22. #17985801 | C22 | semidirect |
| 23. #17985800 | C22 | semidirect |
| 24. (C2×D71)⋊C16 | C22 | semidirect |
| 25. C2×D16×C71 | C22 | semidirect |
| 26. C2×D16×C71 | C22 | semidirect |
| 27. #493×C71 | C22 | semidirect |
| 28. C4×C16×C71 | C22 | semidirect |
| 41. D1136 | D4 | semidirect |
| 69. D568 | C2×D4 | semidirect |
| 90. C16×C71 | C2×D4 | semidirect |
| 110. D284 | D16 | semidirect |
| 128. C2×D71 | C2×D16 | semidirect |
| 130. C4×C71 | C2×D16 | semidirect |
| 144. #2246 | D71 | semidirect |
| 150. C71 | D4×D16 | semidirect |
| 156. C2×D16 | C2×D71 | semidirect |
| 157. C2×D16 | C2×D71 | semidirect |
| 159. #493 | C2×D71 | semidirect |
| 170. C4×C16 | C2×D71 | semidirect |
| 232. C16 | D4×D71 | semidirect |
| 274. C4 | D16×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D71 | 2 |
| #22600015 | 2 |
| #22590423 | 2 |
| #22590372 | 2 |
| #22590250 | 2 |
| C4×D1136 | 2 |
| C16×D284 | 2 |
| C71×#2246 | 2 |
| D4×D16 | 71 |