Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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. D29⋊M32 | C2 | semidirect |
| 2. C2×#11745210 | C2 | semidirect |
| 3. #14272076 | C2 | semidirect |
| 4. #14272075 | C2 | semidirect |
| 8. C29×#135 | C4 | semidirect |
| 10. #11745281 | C4 | semidirect |
| 14. #11745274 | C4 | semidirect |
| 16. #11745266 | C4 | semidirect |
| 37. Q16×C29 | C2×C4 | semidirect |
| 39. D8×C29 | C2×C4 | semidirect |
| 46. Dic116 | C2×C4 | semidirect |
| 47. D232 | C2×C4 | semidirect |
| 118. #135 | #1181 | semidirect |
| 129. C29 | #2139 | semidirect |
| 144. Q16 | C2×#1181 | semidirect |
| 151. D8 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D29⋊M32 | 2 |
| C2×#11745210 | 2 |
| #14272076 | 2 |
| #14272075 | 2 |
| #135×D29 | 2 |
| #2139 | 29 |