Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
488 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14271481 | C2 | semidirect |
| 3. #14271453 | C2 | semidirect |
| 4. #14271358 | C2 | semidirect |
| 5. #14271297 | C2 | semidirect |
| 6. #14271273 | C2 | semidirect |
| 7. #14271220 | 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. #11745156 | C22 | semidirect |
| 31. C4⋊#6597 | C22 | semidirect |
| 32. #11745151 | C22 | semidirect |
| 73. D4×C29 | #41 | semidirect |
| 116. C2×C4×D4 | D29 | semidirect |
| 153. C29 | #3109 | semidirect |
| 199. D4 | #90805 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271713 | 2 |
| #14271481 | 2 |
| #14271453 | 2 |
| #14271358 | 2 |
| #14271297 | 2 |
| #14271273 | 2 |
| #14271220 | 2 |
| C2×C4×D4×C29 | 2 |
| #3109 | 29 |