Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
292 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×C8×#1181 | C2 | semidirect |
| 4. #14272114 | C2 | semidirect |
| 5. #14272037 | C2 | semidirect |
| 6. #14272036 | C2 | semidirect |
| 21. C29×#102 | C4 | semidirect |
| 22. #11745180 | C4 | semidirect |
| 23. #11745169 | C4 | semidirect |
| 24. #11745157 | C4 | semidirect |
| 156. #102 | #1181 | semidirect |
| 159. C29 | #1934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745223 | 2 |
| C2×C8×#1181 | 2 |
| #14272115 | 2 |
| #14272114 | 2 |
| #14272037 | 2 |
| #14272036 | 2 |
| #102×D29 | 2 |
| #1934 | 29 |