Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
712 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 258 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. #14272107 | C2 | direct (N × H) |
| 10. C2×C42×C29 | C4 | semidirect |
| 11. C2×C4×Dic29 | C4 | semidirect |
| 12. C2×C4×Dic29 | C4 | semidirect |
| 13. C42×D29 | C4 | semidirect |
| 32. C42×C29 | C2×C4 | semidirect |
| 33. C4×Dic29 | C2×C4 | semidirect |
| 34. C4×Dic29 | C2×C4 | semidirect |
| 77. C2×C29 | #382 | semidirect |
| 80. D29 | #382 | semidirect |
| 92. C2×C42 | #1181 | semidirect |
| 94. C29 | C2×#382 | semidirect |
| 113. C42 | C2×#1181 | semidirect |
| 154. C2 | #14272107 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#1181 | 2 |
| #14272107 | 2 |
| C2×(C2×#1181)⋊C4 | 2 |
| C2×C42×D29 | 2 |
| C2×#382 | 29 |