Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11745232 | C2 | semidirect |
| 3. #14271518 | C2 | direct (N × H) |
| 4. C2×#11745164 | C2 | semidirect |
| 6. C2×C4×C8×C29 | C2 | semidirect |
| 17. #11745232 | C22 | semidirect |
| 18. C4×C8×C29 | C22 | semidirect |
| 20. #11745164 | C22 | semidirect |
| 75. C2×C4×C8 | D29 | semidirect |
| 76. C2×C29 | #488 | semidirect |
| 93. C4×C8 | C2×D29 | semidirect |
| 94. C29 | C2×#488 | semidirect |
| 144. C2 | #14271518 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745232 | 2 |
| C2×#11745237 | 2 |
| #14271518 | 2 |
| C2×#11745164 | 2 |
| C2×#11745169 | 2 |
| C2×C4×C8×C29 | 2 |
| C2×#488 | 29 |