Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1812 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 277 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×D116 | C2 | semidirect |
| 2. C23×C22⋊D29 | C2 | semidirect |
| 3. C22×#90781 | C2 | semidirect |
| 4. #14271072 | C2 | direct (N × H) |
| 5. C2×#11745179 | C2 | semidirect |
| 6. C22×C22⋊C4×C29 | C2 | semidirect |
| 14. C22×C22⋊D29 | C22 | semidirect |
| 18. C22×D116 | C22 | semidirect |
| 20. C2×C22⋊C4×C29 | C22 | semidirect |
| 22. C2×#90781 | C22 | semidirect |
| 23. #11745179 | C22 | semidirect |
| 28. C24×C29 | D4 | semidirect |
| 37. C23×D29 | D4 | semidirect |
| 42. C22×C4×C29 | D4 | semidirect |
| 51. C22×Dic29 | D4 | semidirect |
| 71. C23×C29 | C2×D4 | semidirect |
| 87. C22×D29 | C2×D4 | semidirect |
| 93. C2×C4×C29 | C2×D4 | semidirect |
| 98. C2×Dic29 | C2×D4 | semidirect |
| 131. C22×C22⋊C4 | D29 | semidirect |
| 135. C2×C29 | #392 | semidirect |
| 157. C2×C22⋊C4 | C2×D29 | semidirect |
| 159. C29 | C2×#392 | semidirect |
| 172. C24 | D116 | semidirect |
| 189. C22×C4 | C22⋊D29 | semidirect |
| 218. C23 | C2×D116 | semidirect |
| 235. C2×C4 | C2×C22⋊D29 | semidirect |
| 265. C2 | #14271072 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D116 | 2 |
| C23×C22⋊D29 | 2 |
| C22×#90781 | 2 |
| #14271072 | 2 |
| C2×#11745179 | 2 |
| C22×C22⋊C4×C29 | 2 |
| C2×#392 | 29 |