Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 197 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×#11745263 | C2 | semidirect |
| 3. #14271242 | C2 | semidirect |
| 4. C8×D116 | C2 | semidirect |
| 5. #14271187 | C2 | semidirect |
| 6. #14271129 | C2 | semidirect |
| 7. C2×C4×C8×C29 | C2 | semidirect |
| 35. C2×C8×C29 | D4 | semidirect |
| 76. C4×C29 | #131 | semidirect |
| 86. C2×C4×C8 | D29 | semidirect |
| 108. C29 | #2931 | semidirect |
| 123. C2×C8 | D116 | semidirect |
| 160. C4 | #11745263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745263 | 2 |
| #14271713 | 2 |
| #14271242 | 2 |
| C8×D116 | 2 |
| #14271187 | 2 |
| #14271129 | 2 |
| C2×C4×C8×C29 | 2 |
| #2931 | 29 |