Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
772 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 145 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. #14271999 | C2 | semidirect |
| 2. #14271730 | C2 | semidirect |
| 3. #14271349 | C2 | semidirect |
| 4. #14271137 | C2 | semidirect |
| 5. #14271136 | C2 | semidirect |
| 6. C29×#535 | C2 | semidirect |
| 8. C22×D4×C29 | C22 | semidirect |
| 20. C29×#120 | C22 | semidirect |
| 21. C29×#117 | C22 | semidirect |
| 22. #11745315 | C22 | semidirect |
| 26. #11745288 | C22 | semidirect |
| 27. #11745182 | C22 | semidirect |
| 28. #11745154 | C22 | semidirect |
| 32. C2×Q8×C29 | D4 | semidirect |
| 38. C2×D4×C29 | D4 | semidirect |
| 40. C22×C4×C29 | D4 | semidirect |
| 59. C2×D116 | D4 | semidirect |
| 61. C2×C4×D29 | D4 | semidirect |
| 63. C2×Dic58 | D4 | semidirect |
| 131. #535 | D29 | semidirect |
| 150. C22×D4 | C2×D29 | semidirect |
| 158. #120 | C2×D29 | semidirect |
| 160. #117 | C2×D29 | semidirect |
| 163. C29 | #3027 | semidirect |
| 180. C2×Q8 | C22⋊D29 | semidirect |
| 193. C2×D4 | C22⋊D29 | semidirect |
| 197. C22×C4 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271999 | 2 |
| #14271730 | 2 |
| #14271349 | 2 |
| #14271137 | 2 |
| #14271136 | 2 |
| C29×#535 | 2 |
| #3027 | 29 |