Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
168 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 2. #14272089 | C2 | direct (N × H) |
| 8. C2×C16×C29 | C4 | semidirect |
| 9. C2×#90768 | C4 | semidirect |
| 10. C16×D29 | C4 | semidirect |
| 22. C16×C29 | C2×C4 | semidirect |
| 23. #90768 | C2×C4 | semidirect |
| 51. C2×C29 | #366 | semidirect |
| 53. D29 | #366 | semidirect |
| 61. C2×C16 | #1181 | semidirect |
| 64. C29 | C2×#366 | semidirect |
| 76. C16 | C2×#1181 | semidirect |
| 103. C2 | #14272089 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745210 | 2 |
| #14272089 | 2 |
| C2×C16×D29 | 2 |
| C2×#366 | 29 |