Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×C4×D116 | C2 | semidirect |
| 2. #14271474 | C2 | semidirect |
| 3. #14271440 | C2 | semidirect |
| 4. #14271355 | C2 | semidirect |
| 5. #14271296 | C2 | semidirect |
| 6. C4×#90782 | C2 | semidirect |
| 7. #14271216 | C2 | semidirect |
| 8. C29×#532 | C2 | semidirect |
| 12. C29×C4⋊Q8 | C22 | semidirect |
| 13. C29×#127 | C22 | semidirect |
| 18. C4×D4×C29 | C22 | semidirect |
| 27. #11745180 | C22 | semidirect |
| 30. #11745155 | C22 | semidirect |
| 31. C4⋊#6597 | C22 | semidirect |
| 32. C4×#6597 | C22 | semidirect |
| 80. C2×C4×C29 | D8 | semidirect |
| 91. D116 | #41 | semidirect |
| 115. #532 | D29 | semidirect |
| 133. C4⋊Q8 | C2×D29 | semidirect |
| 134. #127 | C2×D29 | semidirect |
| 143. C4×D4 | C2×D29 | semidirect |
| 153. C29 | #3100 | semidirect |
| 208. C2×C4 | #90782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D116 | 2 |
| #14271474 | 2 |
| #14271440 | 2 |
| #14271355 | 2 |
| #14271296 | 2 |
| C4×#90782 | 2 |
| #14271216 | 2 |
| C29×#532 | 2 |
| #3100 | 29 |