Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#90785 | C2 | semidirect |
| 3. C2×Q8×Dic29 | C2 | semidirect |
| 4. #14271383 | C2 | direct (N × H) |
| 5. C2×#11745162 | C2 | semidirect |
| 6. C2×#11745164 | C2 | semidirect |
| 18. Q8×Dic29 | C22 | semidirect |
| 20. C2×#90785 | C22 | semidirect |
| 29. #11745164 | C22 | semidirect |
| 30. #11745162 | C22 | semidirect |
| 120. C2×C29 | #464 | semidirect |
| 146. C29 | C2×#464 | semidirect |
| 227. C2 | #14271383 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90785 | 2 |
| C2×#11745298 | 2 |
| C2×Q8×Dic29 | 2 |
| #14271383 | 2 |
| C2×#11745162 | 2 |
| C2×#11745164 | 2 |
| C2×#11745180 | 2 |
| C22×SD16×C29 | 2 |
| C2×#464 | 29 |