Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
572 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 572 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×#11745281 | C2 | semidirect |
| 2. C2×#11745278 | C2 | semidirect |
| 3. C2×#11745274 | C2 | semidirect |
| 4. #14271712 | C2 | semidirect |
| 5. #14271547 | C2 | semidirect |
| 6. #14271545 | C2 | semidirect |
| 7. #14271541 | C2 | semidirect |
| 8. #14271538 | C2 | semidirect |
| 9. #14271534 | C2 | semidirect |
| 10. C4×C8×D29 | C2 | semidirect |
| 11. C29×#495 | C2 | semidirect |
| 75. C8×D29 | D4 | semidirect |
| 76. C8×D29 | D4 | semidirect |
| 120. Dic29 | #135 | semidirect |
| 127. #495 | D29 | semidirect |
| 165. C29 | #3147 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745281 | 2 |
| C2×#11745278 | 2 |
| C2×#11745274 | 2 |
| #14271712 | 2 |
| #14271547 | 2 |
| #14271545 | 2 |
| #14271541 | 2 |
| #14271538 | 2 |
| #14271534 | 2 |
| C4×C8×D29 | 2 |
| C29×#495 | 2 |
| #3147 | 29 |