Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14271968 | C2 | semidirect |
| 2. #14271965 | C2 | semidirect |
| 3. #14271540 | C2 | semidirect |
| 4. #14271434 | C2 | semidirect |
| 5. #14271433 | C2 | semidirect |
| 6. #14271332 | C2 | semidirect |
| 7. #14271281 | C2 | semidirect |
| 8. C29×#443 | C2 | semidirect |
| 9. #11745364 | C22 | semidirect |
| 11. C29×#131 | C22 | semidirect |
| 12. #11745311 | C22 | semidirect |
| 17. #11745270 | C22 | semidirect |
| 21. C2×D232 | C22 | semidirect |
| 22. C2×D232 | C22 | semidirect |
| 23. #11745263 | C22 | semidirect |
| 24. #11745236 | C22 | semidirect |
| 25. C29×#108 | C22 | semidirect |
| 26. C29×#104 | C22 | semidirect |
| 27. C4×C8×C29 | C22 | semidirect |
| 28. #11745171 | C22 | semidirect |
| 29. #11745167 | C22 | semidirect |
| 30. #11745153 | C22 | semidirect |
| 40. Q16×C29 | D4 | semidirect |
| 41. SD16×C29 | D4 | semidirect |
| 42. D8×C29 | D4 | semidirect |
| 52. Dic116 | D4 | semidirect |
| 58. D232 | D4 | semidirect |
| 60. #90773 | D4 | semidirect |
| 106. #443 | D29 | semidirect |
| 126. #131 | C2×D29 | semidirect |
| 129. #108 | C2×D29 | semidirect |
| 131. #104 | C2×D29 | semidirect |
| 133. C4×C8 | C2×D29 | semidirect |
| 134. C29 | #3292 | semidirect |
| 145. Q16 | D116 | semidirect |
| 149. SD16 | D116 | semidirect |
| 157. D8 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271968 | 2 |
| #14271965 | 2 |
| #14271540 | 2 |
| #14271434 | 2 |
| #14271433 | 2 |
| #14271332 | 2 |
| #14271281 | 2 |
| C29×#443 | 2 |
| #3292 | 29 |