Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
1492 conjugacy classes of subgroups; only the 754 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 754 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. #14272232 | C2 | semidirect |
| 2. #14272231 | C2 | semidirect |
| 3. #41×#1181 | C2 | semidirect |
| 4. C2×Q8×#1181 | C2 | semidirect |
| 6. C29×2−1+4 | C4 | semidirect |
| 7. #11745365 | C4 | semidirect |
| 9. #11745362 | C4 | semidirect |
| 21. #41×C29 | C2×C4 | semidirect |
| 22. C2×Q8×C29 | C2×C4 | semidirect |
| 23. #90809 | C2×C4 | semidirect |
| 24. Q8×D29 | C2×C4 | semidirect |
| 26. #90807 | C2×C4 | semidirect |
| 28. #90805 | C2×C4 | semidirect |
| 30. C2×Dic58 | C2×C4 | semidirect |
| 59. #1181 | 2−1+4 | direct (N × H) |
| 74. 2−1+4 | #1181 | direct (N × H) |
| 85. C29 | C4×2−1+4 | semidirect |
| 89. #41 | C2×#1181 | semidirect |
| 93. C2×Q8 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14272232 | 2 |
| #14272231 | 2 |
| #41×#1181 | 2 |
| C2×Q8×#1181 | 2 |
| 2−1+4×D29 | 2 |
| C4×2−1+4 | 29 |