Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
| 3. C2×Q16×D29 | C2 | semidirect |
| 4. #14271738 | C2 | semidirect |
| 5. #14271556 | C2 | semidirect |
| 6. #14271555 | C2 | semidirect |
| 7. #14271548 | C2 | semidirect |
| 8. #14271547 | C2 | semidirect |
| 9. #14271541 | C2 | semidirect |
| 10. #14271117 | C2 | semidirect |
| 11. C29×#494 | C2 | semidirect |
| 127. #494 | D29 | semidirect |
| 161. C29 | #3156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745280 | 2 |
| C2×#11745281 | 2 |
| C2×Q16×D29 | 2 |
| #14271738 | 2 |
| #14271556 | 2 |
| #14271555 | 2 |
| #14271548 | 2 |
| #14271547 | 2 |
| #14271541 | 2 |
| #14271117 | 2 |
| C29×#494 | 2 |
| #3156 | 29 |