Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
464 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 189 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. C2×#11745263 | C2 | semidirect |
| 3. #14271286 | C2 | direct (N × H) |
| 4. C2×#11745167 | C2 | semidirect |
| 5. C2×#11745153 | C2 | semidirect |
| 6. C2×C29×#97 | C2 | semidirect |
| 12. C2×Dic116 | C4 | semidirect |
| 13. #11745266 | C4 | semidirect |
| 15. C2×D232 | C4 | semidirect |
| 16. C2×#90773 | C4 | semidirect |
| 18. #11745263 | C22 | semidirect |
| 21. C29×#97 | C22 | semidirect |
| 22. #11745167 | C22 | semidirect |
| 23. #11745153 | C22 | semidirect |
| 46. Dic116 | C2×C4 | semidirect |
| 47. D232 | C2×C4 | semidirect |
| 48. #90773 | C2×C4 | semidirect |
| 92. C2×#97 | D29 | semidirect |
| 95. C2×C29 | #444 | semidirect |
| 114. #97 | C2×D29 | semidirect |
| 115. C29 | C2×#444 | semidirect |
| 181. C2 | #14271286 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745266 | 2 |
| C2×#11745263 | 2 |
| #14271286 | 2 |
| C2×#11745167 | 2 |
| C2×#11745153 | 2 |
| C2×C29×#97 | 2 |
| C2×#444 | 29 |