Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
464 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 162 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×#11745348 | C2 | semidirect |
| 2. #14272209 | C2 | direct (N × H) |
| 3. C2×#11745211 | C2 | semidirect |
| 4. C2×#11745226 | C2 | semidirect |
| 5. C2×#11745208 | C2 | semidirect |
| 9. #11745348 | C22 | semidirect |
| 15. C2×Q16×C29 | C4 | semidirect |
| 16. C2×#90784 | C4 | semidirect |
| 17. #11745281 | C4 | semidirect |
| 19. C2×D232 | C4 | semidirect |
| 21. #11745226 | C22 | semidirect |
| 22. #11745211 | C22 | semidirect |
| 23. #11745208 | C22 | semidirect |
| 44. Q16×C29 | C2×C4 | semidirect |
| 46. #90784 | C2×C4 | semidirect |
| 48. D232 | C2×C4 | semidirect |
| 93. C2×C29 | #444 | semidirect |
| 101. C2×Q16 | #1181 | semidirect |
| 115. C29 | C2×#444 | semidirect |
| 126. Q16 | C2×#1181 | semidirect |
| 181. C2 | #14272209 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745348 | 2 |
| #14272209 | 2 |
| C2×#11745211 | 2 |
| C2×#11745226 | 2 |
| C2×#11745208 | 2 |
| C2×#11745281 | 2 |
| C2×#444 | 29 |