Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
4038 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 4038 conjugacy classes of subgroups — too many to draw. Only its 827 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. C23×#11765853 | C2 | semidirect |
| 2. C23×#11765850 | C2 | semidirect |
| 3. C22×#14556116 | C2 | semidirect |
| 4. C2×#17986386 | C2 | direct (N × H) |
| 5. C22×#14556039 | C2 | semidirect |
| 6. C22×#127×C71 | C2 | semidirect |
| 10. C22×#11765853 | C22 | semidirect |
| 12. C22×#11765850 | C22 | semidirect |
| 15. C2×#14556116 | C22 | semidirect |
| 17. #17986386 | C22 | direct (N × H) |
| 18. C2×#14556039 | C22 | semidirect |
| 22. C2×#127×C71 | C22 | semidirect |
| 33. C2×#11765853 | C23 | semidirect |
| 35. C2×#11765850 | C23 | semidirect |
| 36. C22×C71⋊C8 | D4 | semidirect |
| 39. #14556116 | C23 | semidirect |
| 41. #14556039 | C23 | semidirect |
| 52. #127×C71 | C23 | semidirect |
| 70. C2×C71⋊C8 | C2×D4 | semidirect |
| 118. C71⋊C8 | C22×D4 | semidirect |
| 122. C22×C71 | #496 | semidirect |
| 135. C2×C71 | C2×#496 | semidirect |
| 141. C22×#127 | D71 | semidirect |
| 145. C71 | C22×#496 | semidirect |
| 156. C2×#127 | C2×D71 | semidirect |
| 187. #127 | C22×D71 | semidirect |
| 264. C22 | #17986386 | direct (N × H) |
| 274. C2 | C2×#17986386 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11765853 | 2 |
| C23×#11765850 | 2 |
| C22×#14556116 | 2 |
| C2×#17986386 | 2 |
| C22×#14556039 | 2 |
| C22×#127×C71 | 2 |
| C22×#496 | 71 |