Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
856 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 218 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. C22×#90796 | C2 | semidirect |
| 2. C22×C4×#1181 | C2 | semidirect |
| 3. C2×#11745226 | C2 | direct (N × H) |
| 6. C22×Q8×C29 | C4 | semidirect |
| 9. C2×#90809 | C4 | semidirect |
| 12. C22×D116 | C4 | semidirect |
| 17. C2×C4×#1181 | C22 | semidirect |
| 19. C2×#90796 | C22 | semidirect |
| 20. #11745226 | C22 | direct (N × H) |
| 26. C2×Q8×C29 | C2×C4 | semidirect |
| 33. #90809 | C2×C4 | semidirect |
| 38. C2×D116 | C2×C4 | semidirect |
| 47. C4×#1181 | C23 | semidirect |
| 49. #90796 | C23 | semidirect |
| 59. Q8×C29 | C22×C4 | semidirect |
| 68. D116 | C22×C4 | semidirect |
| 78. C22×C29 | #104 | semidirect |
| 96. C2×C29 | C2×#104 | semidirect |
| 105. C22×Q8 | #1181 | semidirect |
| 117. C29 | C22×#104 | semidirect |
| 126. C2×Q8 | C2×#1181 | semidirect |
| 154. Q8 | C22×#1181 | semidirect |
| 180. C22 | #11745226 | direct (N × H) |
| 191. C2 | C2×#11745226 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90796 | 2 |
| C22×C4×#1181 | 2 |
| C2×#11745226 | 2 |
| C22×#90809 | 2 |
| C22×#104 | 29 |