Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
400 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 210 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×#11745206 | C2 | semidirect |
| 2. D29⋊M32 | C2 | direct (N × H) |
| 3. C2×#11745214 | C2 | semidirect |
| 4. C2×D29⋊C16 | C2 | semidirect |
| 15. #11745214 | C22 | semidirect |
| 16. C2×#90770 | C22 | semidirect |
| 17. #11745206 | C22 | semidirect |
| 18. D29⋊C16 | C22 | semidirect |
| 41. #90770 | C23 | semidirect |
| 71. C2×D29 | M32 | semidirect |
| 85. C2×C29 | C2×M32 | semidirect |
| 88. D29 | C2×M32 | semidirect |
| 102. C29 | C22×M32 | semidirect |
| 165. C2 | D29⋊M32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745206 | 2 |
| D29⋊M32 | 2 |
| C2×#11745214 | 2 |
| C2×D29⋊C16 | 2 |
| C22×C8×D29 | 2 |
| C22×M32 | 29 |