Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
918 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 918 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22598769 | C2 | semidirect |
| 3. #493×D71 | C2 | semidirect |
| 4. #22590605 | C2 | semidirect |
| 5. #22590597 | C2 | semidirect |
| 6. #22590590 | C2 | semidirect |
| 7. #22590589 | C2 | semidirect |
| 8. C4×#14556067 | C2 | semidirect |
| 9. C71×#2248 | C2 | semidirect |
| 17. C2×#14556071 | C22 | semidirect |
| 18. C2×D1136 | C22 | semidirect |
| 19. C2×#14556069 | C22 | semidirect |
| 22. #17986384 | C22 | semidirect |
| 24. #17986376 | C22 | semidirect |
| 30. #17985774 | C22 | semidirect |
| 31. C4×C71⋊C16 | C22 | semidirect |
| 32. C2×SD32×C71 | C22 | semidirect |
| 33. #494×C71 | C22 | semidirect |
| 35. C4×C16×C71 | C22 | semidirect |
| 64. #14556067 | D4 | semidirect |
| 109. C71⋊C16 | C2×D4 | semidirect |
| 121. C16×C71 | C2×D4 | semidirect |
| 166. C4×C71 | #509 | semidirect |
| 183. #2248 | D71 | semidirect |
| 187. C71 | #33717 | semidirect |
| 196. C2×SD32 | C2×D71 | semidirect |
| 202. #494 | C2×D71 | semidirect |
| 213. C4×C16 | C2×D71 | semidirect |
| 299. C16 | D4×D71 | semidirect |
| 346. C4 | #17986436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17986436 | 2 |
| #22598769 | 2 |
| #493×D71 | 2 |
| #22590605 | 2 |
| #22590597 | 2 |
| #22590590 | 2 |
| #22590589 | 2 |
| C4×#14556067 | 2 |
| C71×#2248 | 2 |
| #33717 | 71 |