Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 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 |
|---|---|---|
| 3. C2×#11745165 | C2 | semidirect |
| 4. C2×#11745156 | C2 | semidirect |
| 5. #106×D29 | C2 | direct (N × H) |
| 6. C2×C29×#106 | C2 | semidirect |
| 14. C2×C8×D29 | C4 | semidirect |
| 18. C29×#106 | C22 | semidirect |
| 19. #11745165 | C22 | semidirect |
| 20. #11745156 | C22 | semidirect |
| 32. C2×C8×C29 | C2×C4 | semidirect |
| 39. C2×#6597 | C2×C4 | semidirect |
| 41. C8×D29 | C2×C4 | semidirect |
| 60. C8×C29 | C22×C4 | semidirect |
| 61. #6597 | C22×C4 | semidirect |
| 66. C2×D29 | #106 | direct (N × H) |
| 80. C2×#106 | D29 | direct (N × H) |
| 81. C2×C29 | C2×#106 | semidirect |
| 84. D29 | C2×#106 | direct (N × H) |
| 98. #106 | C2×D29 | direct (N × H) |
| 99. C29 | C22×#106 | semidirect |
| 114. C2×C8 | C4×D29 | semidirect |
| 140. C8 | C2×C4×D29 | semidirect |
| 154. C2 | #106×D29 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D29 | 2 |
| C2×C4⋊C4×D29 | 2 |
| C2×#11745165 | 2 |
| C2×#11745156 | 2 |
| #106×D29 | 2 |
| C2×C29×#106 | 2 |
| C22×#106 | 29 |