Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
500 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 500 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.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D29 |
| commutator, socle | C22×C29 | C23×C4 |
| Fitting, prime radical | C29×#532 | C2 |
| cosocle | C2×C4×C29 | C24 |
| hypercenter | #532 | D29 |
| hypocenter | C29 | #2931 |
| LCS | G ▷ C22×C29 ▷ C29 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11745310 | C2 | semidirect |
| 2. #14271241 | C2 | semidirect |
| 3. D4×#6597 | C2 | semidirect |
| 4. #14271187 | C2 | semidirect |
| 5. #14271130 | C2 | semidirect |
| 6. C2×C4×#6597 | C2 | semidirect |
| 43. C2×#6597 | D4 | semidirect |
| 77. C4×C29 | #131 | semidirect |
| 108. C29 | #2931 | semidirect |
| 160. C4 | #11745310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745310 | 2 |
| #14271241 | 2 |
| D4×#6597 | 2 |
| #14271187 | 2 |
| #14271130 | 2 |
| C2×C4×#6597 | 2 |
| C29×#532 | 2 |
| #2931 | 29 |