Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
766 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 161 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. #14271670 | C2 | semidirect |
| 2. #14271353 | C2 | semidirect |
| 3. #14271350 | C2 | semidirect |
| 4. #14271137 | C2 | semidirect |
| 5. C29×#585 | C2 | semidirect |
| 11. C22×C4×D29 | C22 | semidirect |
| 14. #11745299 | C22 | semidirect |
| 15. #11745297 | C22 | semidirect |
| 17. #11745288 | C22 | semidirect |
| 18. #11745182 | C22 | semidirect |
| 26. C2×Q8×C29 | D4 | semidirect |
| 29. C2×D4×C29 | D4 | semidirect |
| 32. C22×C4×C29 | D4 | semidirect |
| 79. #585 | D29 | semidirect |
| 101. C29 | #3025 | semidirect |
| 109. C2×Q8 | C22⋊D29 | semidirect |
| 113. C2×D4 | C22⋊D29 | semidirect |
| 119. C22×C4 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271670 | 2 |
| #14271353 | 2 |
| #14271350 | 2 |
| #14271137 | 2 |
| C29×#585 | 2 |
| #3025 | 29 |