Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
496 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D29 | C2 | semidirect |
| 3. C2×#11745308 | C2 | semidirect |
| 4. #14271418 | C2 | semidirect |
| 5. #14271406 | C2 | semidirect |
| 6. #14271401 | C2 | semidirect |
| 7. #14271389 | C2 | semidirect |
| 8. #14271205 | C2 | semidirect |
| 9. #14271172 | C2 | semidirect |
| 10. #14271164 | C2 | semidirect |
| 11. C2×C29×#137 | C2 | semidirect |
| 16. C2×Q16×C29 | C22 | semidirect |
| 17. C2×SD16×C29 | C22 | semidirect |
| 39. #11745183 | C22 | semidirect |
| 40. #11745183 | C22 | semidirect |
| 41. #11745183 | C22 | semidirect |
| 42. #11745180 | C22 | semidirect |
| 43. #11745166 | C22 | semidirect |
| 44. #11745165 | C22 | semidirect |
| 70. M16×C29 | D4 | semidirect |
| 146. C2×D29 | #137 | semidirect |
| 157. C2×#137 | D29 | semidirect |
| 179. C2×Q16 | C2×D29 | semidirect |
| 180. C2×SD16 | C2×D29 | semidirect |
| 208. C29 | #3056 | semidirect |
| 236. M16 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D29 | 2 |
| #14271670 | 2 |
| C2×#11745308 | 2 |
| #14271418 | 2 |
| #14271406 | 2 |
| #14271401 | 2 |
| #14271389 | 2 |
| #14271205 | 2 |
| #14271172 | 2 |
| #14271164 | 2 |
| C2×C29×#137 | 2 |
| #3056 | 29 |