Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
346 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 66 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. #14272230 | C2 | semidirect |
| 2. #14272162 | C2 | semidirect |
| 3. #14272155 | C2 | semidirect |
| 4. #14272144 | C2 | semidirect |
| 5. #14272045 | C2 | semidirect |
| 6. #14272031 | C2 | semidirect |
| 17. C2×SD16×C29 | C4 | semidirect |
| 18. C2×#90784 | C4 | semidirect |
| 19. C2×#90782 | C4 | semidirect |
| 22. C2×D232 | C4 | semidirect |
| 29. C2×Q8×C29 | C2×C4 | semidirect |
| 42. C2×D116 | C2×C4 | semidirect |
| 59. C2×C8×C29 | C2×C4 | semidirect |
| 62. C2×#6597 | C2×C4 | semidirect |
| 141. C2×SD16 | #1181 | semidirect |
| 155. C29 | #1904 | semidirect |
| 161. C2×Q8 | C2×#1181 | semidirect |
| 184. C2×C8 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272230 | 2 |
| #14272162 | 2 |
| #14272155 | 2 |
| #14272144 | 2 |
| #14272045 | 2 |
| #14272031 | 2 |
| C2×#11745276 | 2 |
| #1904 | 29 |