Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
476 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 200 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. #14272174 | C2 | semidirect |
| 3. #14272173 | C2 | semidirect |
| 4. C2×#11745209 | C2 | semidirect |
| 11. C29×#131 | C4 | semidirect |
| 12. #11745310 | C4 | semidirect |
| 13. #11745269 | C4 | semidirect |
| 15. #11745263 | C4 | semidirect |
| 34. M16×C29 | C2×C4 | semidirect |
| 35. C2×C8×C29 | C2×C4 | semidirect |
| 36. #90777 | C2×C4 | semidirect |
| 37. C2×#6597 | C2×C4 | semidirect |
| 38. #90772 | C2×C4 | semidirect |
| 39. C8×D29 | C2×C4 | semidirect |
| 40. C8×D29 | C2×C4 | semidirect |
| 86. #131 | #1181 | semidirect |
| 97. C29 | #2912 | semidirect |
| 108. M16 | C2×#1181 | semidirect |
| 114. C2×C8 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272232 | 2 |
| #14272174 | 2 |
| #14272173 | 2 |
| C2×#11745209 | 2 |
| #131×D29 | 2 |
| #2912 | 29 |