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×#11745209 | C2 | semidirect |
| 3. #14272080 | C2 | semidirect |
| 4. #14272079 | C2 | semidirect |
| 8. C29×#135 | C4 | semidirect |
| 11. Q16×D29 | C4 | semidirect |
| 15. D8×D29 | C4 | semidirect |
| 16. #11745266 | C4 | semidirect |
| 20. #11745209 | C22 | semidirect |
| 21. #11745206 | C22 | semidirect |
| 37. Q16×C29 | C2×C4 | semidirect |
| 39. D8×C29 | C2×C4 | semidirect |
| 46. Dic116 | C2×C4 | semidirect |
| 47. D232 | C2×C4 | semidirect |
| 108. D29 | #360 | semidirect |
| 115. #135 | #1181 | semidirect |
| 126. C29 | C2×#360 | semidirect |
| 141. Q16 | C2×#1181 | semidirect |
| 148. 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×#11745209 | 2 |
| #14272080 | 2 |
| #14272079 | 2 |
| #135×D29 | 2 |
| C2×#360 | 29 |