Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 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. #14271713 | C2 | semidirect |
| 2. #14271476 | C2 | semidirect |
| 3. #14271443 | C2 | semidirect |
| 4. #14271358 | C2 | semidirect |
| 5. #14271297 | C2 | semidirect |
| 6. C4×#90782 | C2 | semidirect |
| 7. #14271216 | C2 | semidirect |
| 8. C2×C4×D4×C29 | C2 | semidirect |
| 23. #11745236 | C22 | semidirect |
| 25. C4×D116 | C22 | semidirect |
| 26. #11745231 | C22 | semidirect |
| 29. #11745157 | C22 | semidirect |
| 30. #11745155 | C22 | semidirect |
| 31. C4⋊#6597 | C22 | semidirect |
| 32. C4×#6597 | C22 | semidirect |
| 73. D4×C29 | #41 | semidirect |
| 80. C2×C4×C29 | D8 | semidirect |
| 116. C2×C4×D4 | D29 | semidirect |
| 153. C29 | #3100 | semidirect |
| 199. D4 | #90805 | 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 |
|---|---|
| #14271713 | 2 |
| #14271476 | 2 |
| #14271443 | 2 |
| #14271358 | 2 |
| #14271297 | 2 |
| C4×#90782 | 2 |
| #14271216 | 2 |
| C2×C4×D4×C29 | 2 |
| #3100 | 29 |