Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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×#11745215 | C2 | semidirect |
| 2. #14272069 | C2 | semidirect |
| 3. #14272067 | C2 | semidirect |
| 5. C2×#41×C29 | C4 | semidirect |
| 8. #11745309 | C4 | semidirect |
| 10. #11745302 | C4 | semidirect |
| 14. #11745288 | C4 | semidirect |
| 20. C2×Q8×C29 | C2×C4 | semidirect |
| 22. C2×D4×C29 | C2×C4 | semidirect |
| 37. C4×Dic29 | C2×C4 | semidirect |
| 38. C4×Dic29 | C2×C4 | semidirect |
| 91. C2×#41 | #1181 | semidirect |
| 103. C29 | #2127 | semidirect |
| 106. C2×Q8 | C2×#1181 | semidirect |
| 114. C2×D4 | C2×#1181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745215 | 2 |
| #14272069 | 2 |
| #14272067 | 2 |
| #14271727 | 2 |
| #2127 | 29 |