Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 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. #14272209 | C2 | semidirect |
| 2. #14272204 | C2 | semidirect |
| 3. #14272088 | C2 | semidirect |
| 4. #14272081 | C2 | semidirect |
| 5. #14272080 | C2 | semidirect |
| 6. #14272053 | C2 | semidirect |
| 18. C29×SD32 | C4 | semidirect |
| 19. #11745176 | C4 | semidirect |
| 20. #11745174 | C4 | semidirect |
| 21. D464 | C4 | semidirect |
| 33. Q16×C29 | C2×C4 | semidirect |
| 38. D232 | C2×C4 | semidirect |
| 41. C16×C29 | C2×C4 | semidirect |
| 42. #90768 | C2×C4 | semidirect |
| 88. SD32 | #1181 | semidirect |
| 98. C29 | AGL(1,ℤ/16) | semidirect |
| 102. Q16 | C2×#1181 | semidirect |
| 118. C16 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272209 | 2 |
| #14272204 | 2 |
| #14272088 | 2 |
| #14272081 | 2 |
| #14272080 | 2 |
| #14272053 | 2 |
| #14271600 | 2 |
| AGL(1,ℤ/16) | 29 |