Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
324 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 70 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×#11745346 | C2 | semidirect |
| 2. C2×#11745226 | C2 | semidirect |
| 3. C2×#11745224 | C2 | semidirect |
| 4. #14272138 | C2 | semidirect |
| 5. #14272039 | C2 | semidirect |
| 6. (C2×#1181)⋊C8 | C2 | semidirect |
| 18. C2×SD16×C29 | C4 | semidirect |
| 19. C2×#90785 | C4 | semidirect |
| 20. C2×#90782 | C4 | semidirect |
| 23. C2×#90773 | C4 | semidirect |
| 144. C2×SD16 | #1181 | semidirect |
| 159. C29 | #1876 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745346 | 2 |
| C2×#11745226 | 2 |
| C2×#11745224 | 2 |
| #14272138 | 2 |
| #14272039 | 2 |
| (C2×#1181)⋊C8 | 2 |
| C2×#11745278 | 2 |
| #1876 | 29 |