Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745362 | C2 | semidirect |
| 2. C2×#11745294 | C2 | semidirect |
| 3. #14271730 | C2 | semidirect |
| 4. #14271307 | C2 | semidirect |
| 5. #14271300 | C2 | semidirect |
| 6. #14271172 | C2 | semidirect |
| 7. #14271160 | C2 | semidirect |
| 8. #14271129 | C2 | semidirect |
| 9. C22×SD16×C29 | C2 | semidirect |
| 15. C2×#90809 | C22 | semidirect |
| 17. C2×Q8×D29 | C22 | semidirect |
| 33. #11745183 | C22 | semidirect |
| 34. #11745169 | C22 | semidirect |
| 35. #11745168 | C22 | semidirect |
| 36. #11745164 | C22 | semidirect |
| 40. C2×Q8×C29 | D4 | semidirect |
| 61. #90805 | D4 | semidirect |
| 142. C22×SD16 | D29 | semidirect |
| 182. C29 | #3010 | semidirect |
| 200. C2×Q8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745362 | 2 |
| C2×#11745294 | 2 |
| #14271730 | 2 |
| #14271307 | 2 |
| #14271300 | 2 |
| #14271172 | 2 |
| #14271160 | 2 |
| #14271129 | 2 |
| C22×SD16×C29 | 2 |
| #3010 | 29 |