Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
360 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. #14271187 | C2 | semidirect |
| 3. C2×#11745153 | C2 | semidirect |
| 4. C43×C29 | C2 | semidirect |
| 11. #11745237 | C4 | semidirect |
| 12. #11745236 | C4 | semidirect |
| 14. #11745231 | C4 | semidirect |
| 32. C42×C29 | D4 | semidirect |
| 64. C4×C29 | #104 | semidirect |
| 72. C43 | D29 | semidirect |
| 89. C29 | #1962 | semidirect |
| 109. C42 | D116 | semidirect |
| 137. C4 | #11745153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271713 | 2 |
| #14271187 | 2 |
| C2×#11745153 | 2 |
| C43×C29 | 2 |
| #1962 | 29 |