Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
572 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#11745271 | C2 | semidirect |
| 2. C2×#11745270 | C2 | semidirect |
| 3. #14271713 | C2 | semidirect |
| 4. C2×#11745237 | C2 | semidirect |
| 5. #14271557 | C2 | semidirect |
| 6. #14271552 | C2 | semidirect |
| 7. #14271547 | C2 | semidirect |
| 8. C4×M16×C29 | C2 | semidirect |
| 18. C2×Dic116 | C22 | semidirect |
| 21. C2×#90773 | C22 | semidirect |
| 25. #11745237 | C22 | semidirect |
| 26. #11745236 | C22 | semidirect |
| 28. #11745231 | C22 | semidirect |
| 29. C29×#97 | C22 | semidirect |
| 30. C4×C8×C29 | C22 | semidirect |
| 48. M16×C29 | D4 | semidirect |
| 109. C4×M16 | D29 | semidirect |
| 135. #97 | C2×D29 | semidirect |
| 136. C4×C8 | C2×D29 | semidirect |
| 137. C29 | #3153 | semidirect |
| 159. M16 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745271 | 2 |
| C2×#11745270 | 2 |
| #14271713 | 2 |
| C2×#11745237 | 2 |
| #14271557 | 2 |
| #14271552 | 2 |
| #14271547 | 2 |
| C4×M16×C29 | 2 |
| #3153 | 29 |