Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
572 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 153 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×#11745266 | C2 | semidirect |
| 2. C2×#11745312 | C2 | semidirect |
| 3. #14271709 | C2 | semidirect |
| 4. #14271548 | C2 | semidirect |
| 5. #14271546 | C2 | semidirect |
| 6. #14271544 | C2 | semidirect |
| 7. #14271541 | C2 | semidirect |
| 8. #14271538 | C2 | semidirect |
| 9. #14271534 | C2 | semidirect |
| 10. C2×C8×Dic29 | C2 | semidirect |
| 11. C2×C29×#135 | C2 | semidirect |
| 58. C2×C8×C29 | D4 | semidirect |
| 71. C2×#6597 | D4 | semidirect |
| 120. Dic29 | #135 | semidirect |
| 123. C2×#135 | D29 | semidirect |
| 165. C29 | #3147 | semidirect |
| 194. C2×C8 | C22⋊D29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745266 | 2 |
| C2×#11745312 | 2 |
| #14271709 | 2 |
| #14271548 | 2 |
| #14271546 | 2 |
| #14271544 | 2 |
| #14271541 | 2 |
| #14271538 | 2 |
| #14271534 | 2 |
| C2×C8×Dic29 | 2 |
| C2×C29×#135 | 2 |
| #3147 | 29 |