Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11745280 | C2 | semidirect |
| 2. C2×#11745277 | C2 | semidirect |
| 4. C4⋊Q8×D29 | C2 | semidirect |
| 5. #14271558 | C2 | semidirect |
| 6. #14271557 | C2 | semidirect |
| 7. #14271555 | C2 | semidirect |
| 8. #14271541 | C2 | semidirect |
| 9. #14271534 | C2 | semidirect |
| 10. #14271115 | C2 | semidirect |
| 11. C29×#497 | C2 | semidirect |
| 79. #90772 | D4 | semidirect |
| 125. Dic29 | #137 | semidirect |
| 133. #497 | D29 | semidirect |
| 171. C29 | #3152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745280 | 2 |
| C2×#11745277 | 2 |
| #14271712 | 2 |
| C4⋊Q8×D29 | 2 |
| #14271558 | 2 |
| #14271557 | 2 |
| #14271555 | 2 |
| #14271541 | 2 |
| #14271534 | 2 |
| #14271115 | 2 |
| C29×#497 | 2 |
| #3152 | 29 |