Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
608 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 170 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×D4×#1181 | C2 | semidirect |
| 2. #14272204 | C2 | direct (N × H) |
| 3. C2×#11745209 | C2 | semidirect |
| 4. C2×#11745223 | C2 | semidirect |
| 5. C2×#11745208 | C2 | semidirect |
| 11. D4×#1181 | C22 | semidirect |
| 15. C2×D8×C29 | C4 | semidirect |
| 16. C2×#90782 | C4 | semidirect |
| 17. D8×D29 | C4 | semidirect |
| 19. C2×D232 | C4 | semidirect |
| 21. #11745223 | C22 | semidirect |
| 22. #11745209 | C22 | semidirect |
| 23. #11745208 | C22 | semidirect |
| 29. C2×D4×C29 | C2×C4 | semidirect |
| 33. D4×D29 | C2×C4 | semidirect |
| 35. C2×D116 | C2×C4 | semidirect |
| 45. D8×C29 | C2×C4 | semidirect |
| 46. C2×C8×C29 | C2×C4 | semidirect |
| 47. #90782 | C2×C4 | semidirect |
| 48. C2×#6597 | C2×C4 | semidirect |
| 49. D232 | C2×C4 | semidirect |
| 50. C8×D29 | C2×C4 | semidirect |
| 65. D4×C29 | C22×C4 | semidirect |
| 71. D116 | C22×C4 | semidirect |
| 77. C8×C29 | C22×C4 | semidirect |
| 78. #6597 | C22×C4 | semidirect |
| 104. C2×C29 | #442 | semidirect |
| 107. D29 | #442 | semidirect |
| 115. C2×D8 | #1181 | semidirect |
| 126. C29 | C2×#442 | semidirect |
| 134. C2×D4 | C2×#1181 | semidirect |
| 142. D8 | C2×#1181 | semidirect |
| 149. C2×C8 | C2×#1181 | semidirect |
| 167. D4 | C22×#1181 | semidirect |
| 181. C8 | C22×#1181 | semidirect |
| 203. C2 | #14272204 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#1181 | 2 |
| #14272204 | 2 |
| C2×#11745209 | 2 |
| C2×#11745223 | 2 |
| C2×#11745208 | 2 |
| C2×D8×D29 | 2 |
| C2×#442 | 29 |