Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
230 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 60 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. #14272170 | C2 | semidirect |
| 4. C2×C8×#1181 | C2 | semidirect |
| 5. #14272039 | C2 | semidirect |
| 6. #14272033 | C2 | semidirect |
| 21. C29×#102 | C4 | semidirect |
| 22. #11745180 | C4 | semidirect |
| 23. #11745164 | C4 | semidirect |
| 24. #11745158 | C4 | semidirect |
| 126. #102 | #1181 | semidirect |
| 130. C29 | #1937 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272170 | 2 |
| C2×#11745224 | 2 |
| #14272137 | 2 |
| C2×C8×#1181 | 2 |
| #14272039 | 2 |
| #14272033 | 2 |
| #14271156 | 2 |
| #1937 | 29 |