Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14271718 | C2 | semidirect |
| 3. #14271525 | C2 | semidirect |
| 4. #14271523 | C2 | semidirect |
| 5. #14271522 | C2 | semidirect |
| 6. #14271519 | C2 | semidirect |
| 7. #14271516 | C2 | semidirect |
| 8. #14271170 | C2 | semidirect |
| 10. #14271115 | C2 | semidirect |
| 11. C29×#489 | C2 | semidirect |
| 14. C29×C4⋊Q8 | C22 | semidirect |
| 23. #11745252 | C22 | semidirect |
| 31. #11745231 | C22 | semidirect |
| 32. C29×#103 | C22 | semidirect |
| 34. C29×#97 | C22 | semidirect |
| 35. #11745183 | C22 | semidirect |
| 38. #11745164 | C22 | semidirect |
| 39. C8×Dic29 | C22 | semidirect |
| 40. #11745158 | C22 | semidirect |
| 42. #11745151 | C22 | semidirect |
| 138. #489 | D29 | semidirect |
| 154. C4⋊Q8 | C2×D29 | semidirect |
| 173. #103 | C2×D29 | semidirect |
| 179. #97 | C2×D29 | semidirect |
| 181. C29 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271718 | 2 |
| #124×D29 | 2 |
| #14271525 | 2 |
| #14271523 | 2 |
| #14271522 | 2 |
| #14271519 | 2 |
| #14271516 | 2 |
| #14271170 | 2 |
| #14271166 | 2 |
| #14271115 | 2 |
| C29×#489 | 2 |
| #3140 | 29 |