Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
760 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745271 | C2 | semidirect |
| 3. C2×#11745313 | C2 | semidirect |
| 4. C2×#11745237 | C2 | semidirect |
| 5. #14271342 | C2 | direct (N × H) |
| 6. C2×#11745153 | C2 | semidirect |
| 7. C2×#11745171 | C2 | semidirect |
| 8. C2×C29×#104 | C2 | semidirect |
| 21. C22×Dic58 | C22 | semidirect |
| 22. C2×M16×C29 | C22 | semidirect |
| 23. C2×C42×C29 | C22 | semidirect |
| 25. #11745313 | C22 | semidirect |
| 29. C2×#90777 | C22 | semidirect |
| 31. #11745271 | C22 | semidirect |
| 35. #11745237 | C22 | semidirect |
| 36. C29×#104 | C22 | semidirect |
| 37. #11745171 | C22 | semidirect |
| 38. #11745153 | C22 | semidirect |
| 84. C2×Dic58 | C23 | semidirect |
| 86. M16×C29 | C23 | semidirect |
| 89. C42×C29 | C23 | semidirect |
| 94. #90777 | C23 | semidirect |
| 177. C2×#104 | D29 | semidirect |
| 182. C2×C29 | #455 | semidirect |
| 208. C2×M16 | C2×D29 | semidirect |
| 212. C2×C42 | C2×D29 | semidirect |
| 214. #104 | C2×D29 | semidirect |
| 216. C29 | C2×#455 | semidirect |
| 270. M16 | C22×D29 | semidirect |
| 275. C42 | C22×D29 | semidirect |
| 353. C2 | #14271342 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745364 | 2 |
| C2×#11745271 | 2 |
| C2×#11745313 | 2 |
| C2×#11745237 | 2 |
| #14271342 | 2 |
| C2×#11745153 | 2 |
| C2×#11745171 | 2 |
| C2×C29×#104 | 2 |
| C2×#455 | 29 |