Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. #14271418 | C2 | direct (N × H) |
| 4. C2×#11745165 | C2 | semidirect |
| 5. C2×#11745183 | C2 | semidirect |
| 6. C22×Q16×C29 | C2 | semidirect |
| 10. C2×Q16×C29 | C22 | semidirect |
| 20. #11745183 | C22 | semidirect |
| 21. #11745165 | C22 | semidirect |
| 80. C22×Q16 | D29 | semidirect |
| 86. C2×C29 | #470 | semidirect |
| 93. C2×Q16 | C2×D29 | semidirect |
| 105. C29 | C2×#470 | semidirect |
| 164. C2 | #14271418 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90772 | 2 |
| C2×#11745308 | 2 |
| #14271418 | 2 |
| C2×#11745165 | 2 |
| C2×#11745183 | 2 |
| C22×Q16×C29 | 2 |
| C2×#470 | 29 |