Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
592 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 181 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. C22×Dic116 | C2 | semidirect |
| 2. C22×#90773 | C2 | semidirect |
| 4. C2×#11745237 | C2 | semidirect |
| 5. #14271547 | C2 | direct (N × H) |
| 6. C2×C4×C8×C29 | C2 | semidirect |
| 14. C2×Dic116 | C22 | semidirect |
| 18. C2×#90773 | C22 | semidirect |
| 20. #11745237 | C22 | semidirect |
| 21. C4×C8×C29 | C22 | semidirect |
| 81. C2×C4×C8 | D29 | semidirect |
| 82. C2×C29 | #495 | semidirect |
| 100. C4×C8 | C2×D29 | semidirect |
| 101. C29 | C2×#495 | semidirect |
| 156. C2 | #14271547 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic116 | 2 |
| C22×#90773 | 2 |
| C22×D232 | 2 |
| C2×#11745237 | 2 |
| #14271547 | 2 |
| C2×C4×C8×C29 | 2 |
| C2×#495 | 29 |