Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
2774 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 2774 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
|---|---|---|
| 2. C22×#14556043 | C2 | semidirect |
| 3. C2×#17985787 | C2 | direct (N × H) |
| 4. C22×#100×C71 | C2 | semidirect |
| 5. C25×D71 | C4 | semidirect |
| 9. C2×#14556096 | C4 | semidirect |
| 12. C22×C22⋊Dic71 | C4 | semidirect |
| 15. C2×#14556043 | C22 | semidirect |
| 16. #17985787 | C22 | direct (N × H) |
| 20. C2×#100×C71 | C22 | semidirect |
| 26. C24×D71 | C2×C4 | semidirect |
| 35. #14556096 | C2×C4 | semidirect |
| 40. C2×C22⋊Dic71 | C2×C4 | semidirect |
| 44. #14556043 | C23 | semidirect |
| 58. #100×C71 | C23 | semidirect |
| 74. C23×D71 | C22×C4 | semidirect |
| 86. C22⋊Dic71 | C22×C4 | semidirect |
| 196. C22×C71 | AΣL(1,𝔽16) | semidirect |
| 219. C2×C71 | C2×AΣL(1,𝔽16) | semidirect |
| 223. C22×#100 | D71 | semidirect |
| 226. C71 | C22×AΣL(1,𝔽16) | semidirect |
| 239. C2×#100 | C2×D71 | semidirect |
| 278. #100 | C22×D71 | semidirect |
| 426. C22 | #17985787 | direct (N × H) |
| 441. C2 | C2×#17985787 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14556096 | 2 |
| C22×#14556043 | 2 |
| C2×#17985787 | 2 |
| C22×#100×C71 | 2 |
| C22×AΣL(1,𝔽16) | 71 |