Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
924 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 277 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 |
|---|---|---|
| 2. C2×C4×D116 | C2 | semidirect |
| 3. #14271065 | C2 | semidirect |
| 4. #14271033 | C2 | semidirect |
| 5. C43×C29 | C2 | semidirect |
| 13. #11745236 | C4 | direct (N × H) |
| 22. C2×D116 | C2×C4 | semidirect |
| 25. C42×C29 | C2×C4 | semidirect |
| 26. C42×C29 | D4 | semidirect |
| 50. C4×C29 | C4×D4 | semidirect |
| 51. C4×C29 | #127 | semidirect |
| 57. C43 | D29 | semidirect |
| 71. C29 | C4×#127 | semidirect |
| 84. C42 | C4×D29 | semidirect |
| 85. C42 | D116 | semidirect |
| 107. C4 | C4×D116 | semidirect |
| 108. C4 | #11745236 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745236 | 2 |
| C2×C4×D116 | 2 |
| #14271065 | 2 |
| #14271033 | 2 |
| C43×C29 | 2 |
| C4×#127 | 29 |