Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#11745362 | C2 | semidirect |
| 2. #14271961 | C2 | semidirect |
| 3. #14271345 | C2 | semidirect |
| 4. #14271335 | C2 | semidirect |
| 5. #14271181 | C2 | semidirect |
| 6. C2×#11745184 | C2 | semidirect |
| 7. C29×#536 | C2 | semidirect |
| 17. C29×C4⋊Q8 | C22 | semidirect |
| 18. C29×#124 | C22 | semidirect |
| 25. #11745304 | C22 | semidirect |
| 26. #11745294 | C22 | semidirect |
| 28. #11745184 | C22 | semidirect |
| 29. #11745153 | C22 | semidirect |
| 120. #536 | D29 | semidirect |
| 146. C4⋊Q8 | C2×D29 | semidirect |
| 147. #124 | C2×D29 | semidirect |
| 153. C29 | #3020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745362 | 2 |
| #14271961 | 2 |
| #14271345 | 2 |
| #14271335 | 2 |
| #14271181 | 2 |
| C2×#11745184 | 2 |
| C29×#536 | 2 |
| #3020 | 29 |