Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
340 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 78 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×#11745210 | C2 | semidirect |
| 2. C2×#11745225 | C2 | semidirect |
| 4. C2×#11745208 | C2 | semidirect |
| 5. (C2×#1181)⋊Q8 | C2 | semidirect |
| 15. C2×SD16×C29 | C4 | semidirect |
| 16. C2×#90784 | C4 | semidirect |
| 17. C2×#90783 | C4 | semidirect |
| 20. C2×#90773 | C4 | semidirect |
| 102. C8×C29 | C22⋊C4 | semidirect |
| 103. #6597 | C22⋊C4 | semidirect |
| 147. C2×SD16 | #1181 | semidirect |
| 159. C29 | #1973 | semidirect |
| 236. C8 | C22⋊#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745210 | 2 |
| C2×#11745225 | 2 |
| C2×#11745223 | 2 |
| C2×#11745208 | 2 |
| (C2×#1181)⋊Q8 | 2 |
| #14272115 | 2 |
| C2×SD16×D29 | 2 |
| #1973 | 29 |