Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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×D232 | C2 | semidirect |
| 2. #14271598 | C2 | direct (N × H) |
| 3. C2×#11745176 | C2 | semidirect |
| 4. C2×#11745174 | C2 | semidirect |
| 5. C2×#11745160 | C2 | semidirect |
| 6. C2×C29×#135 | C2 | semidirect |
| 10. C29×#135 | C22 | semidirect |
| 11. C2×Q16×C29 | C22 | semidirect |
| 13. C2×D8×C29 | C22 | semidirect |
| 18. C2×D232 | C22 | semidirect |
| 19. #11745176 | C22 | semidirect |
| 20. #11745174 | C22 | semidirect |
| 21. #11745160 | C22 | semidirect |
| 22. C2×#90768 | C22 | semidirect |
| 36. Q16×C29 | C23 | semidirect |
| 39. D8×C29 | C23 | semidirect |
| 47. #90768 | C23 | semidirect |
| 83. C2×#135 | D29 | semidirect |
| 91. C2×C29 | #509 | semidirect |
| 97. #135 | C2×D29 | semidirect |
| 98. C2×Q16 | C2×D29 | semidirect |
| 104. C2×D8 | C2×D29 | semidirect |
| 110. C29 | C2×#509 | semidirect |
| 124. Q16 | C22×D29 | semidirect |
| 130. D8 | C22×D29 | semidirect |
| 173. C2 | #14271598 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D232 | 2 |
| #14271598 | 2 |
| C2×#11745176 | 2 |
| C2×#11745174 | 2 |
| C2×#11745160 | 2 |
| C2×C29×#135 | 2 |
| C2×#509 | 29 |