Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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×#11745271 | C2 | semidirect |
| 3. C2×#11745237 | C2 | semidirect |
| 4. C2×#11745153 | C2 | semidirect |
| 5. #14271171 | C2 | semidirect |
| 6. C2×#11745171 | C2 | semidirect |
| 7. C29×#339 | C2 | semidirect |
| 53. C2×Dic58 | D4 | semidirect |
| 55. M16×C29 | D4 | semidirect |
| 61. C42×C29 | D4 | semidirect |
| 132. #339 | D29 | semidirect |
| 160. C29 | #2004 | semidirect |
| 191. M16 | D116 | semidirect |
| 200. C42 | D116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745271 | 2 |
| #14271732 | 2 |
| C2×#11745237 | 2 |
| C2×#11745153 | 2 |
| #14271171 | 2 |
| C2×#11745171 | 2 |
| C29×#339 | 2 |
| #2004 | 29 |