Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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×#11745313 | C2 | semidirect |
| 2. C2×M16×D29 | C2 | semidirect |
| 4. C2×#11745259 | C2 | semidirect |
| 5. #14271420 | C2 | semidirect |
| 6. #14271408 | C2 | semidirect |
| 7. #14271403 | C2 | semidirect |
| 8. #14271391 | C2 | semidirect |
| 9. #14271203 | C2 | semidirect |
| 10. #14271173 | C2 | semidirect |
| 11. C29×#417 | C2 | semidirect |
| 20. C2×#90785 | C22 | semidirect |
| 25. C2×#90783 | C22 | semidirect |
| 39. C29×#103 | C22 | semidirect |
| 40. C29×#102 | C22 | semidirect |
| 41. #11745164 | C22 | semidirect |
| 42. #11745164 | C22 | semidirect |
| 43. #11745156 | C22 | semidirect |
| 44. #11745155 | C22 | semidirect |
| 88. #90777 | D4 | semidirect |
| 146. C2×D29 | #137 | semidirect |
| 167. #417 | D29 | semidirect |
| 206. #103 | C2×D29 | semidirect |
| 207. #102 | C2×D29 | semidirect |
| 208. C29 | #3056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745313 | 2 |
| C2×M16×D29 | 2 |
| #14271670 | 2 |
| C2×#11745259 | 2 |
| #14271420 | 2 |
| #14271408 | 2 |
| #14271403 | 2 |
| #14271391 | 2 |
| #14271203 | 2 |
| #14271173 | 2 |
| C29×#417 | 2 |
| #3056 | 29 |