Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
712 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 147 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×#17986433 | C2 | semidirect |
| 2. #22600026 | C2 | semidirect |
| 3. #22590601 | C2 | semidirect |
| 4. #22590454 | C2 | semidirect |
| 5. #22590395 | C2 | semidirect |
| 6. #22590281 | C2 | semidirect |
| 7. #22590253 | C2 | semidirect |
| 8. #22590173 | C2 | semidirect |
| 9. C4×D16×C71 | C2 | semidirect |
| 11. C2×D8×D71 | C22 | semidirect |
| 14. C2×Dic568 | C22 | semidirect |
| 15. C2×#14556073 | C22 | semidirect |
| 16. C2×#14556072 | C22 | semidirect |
| 19. C2×#14556067 | C22 | semidirect |
| 20. #17986383 | C22 | semidirect |
| 21. #17986241 | C22 | semidirect |
| 27. C4⋊(C71⋊C16) | C22 | semidirect |
| 28. #17985802 | C22 | semidirect |
| 29. #17985799 | C22 | semidirect |
| 30. (C2×D71)⋊C16 | C22 | semidirect |
| 32. C4×D8×C71 | C22 | semidirect |
| 33. #366×C71 | C22 | semidirect |
| 34. #357×C71 | C22 | semidirect |
| 35. C4×C16×C71 | C22 | semidirect |
| 69. D16×C71 | D4 | semidirect |
| 179. C4×D16 | D71 | semidirect |
| 181. C71 | #33839 | semidirect |
| 199. C4×D8 | C2×D71 | semidirect |
| 201. #366 | C2×D71 | semidirect |
| 205. #357 | C2×D71 | semidirect |
| 207. C4×C16 | C2×D71 | semidirect |
| 235. D16 | D284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986433 | 2 |
| #22600026 | 2 |
| #22590601 | 2 |
| #22590454 | 2 |
| #22590395 | 2 |
| #22590281 | 2 |
| #22590253 | 2 |
| #22590173 | 2 |
| C4×D16×C71 | 2 |
| #33839 | 71 |