Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
412 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 229 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. #14271224 | C2 | direct (N × H) |
| 2. C2×C4⋊#6597 | C2 | semidirect |
| 4. C2×#11745151 | C2 | semidirect |
| 5. C2×C4×#6597 | C2 | semidirect |
| 17. C4⋊#6597 | C22 | semidirect |
| 18. #11745151 | C22 | semidirect |
| 19. C4×#6597 | C22 | semidirect |
| 74. C2×C29 | #433 | semidirect |
| 90. C29 | C2×#433 | semidirect |
| 138. C2 | #14271224 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14271224 | 2 |
| C2×C4⋊#6597 | 2 |
| C2×C22⋊#6597 | 2 |
| C2×#11745151 | 2 |
| C2×C4×#6597 | 2 |
| C2×C29×#117 | 2 |
| C2×#433 | 29 |