Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
124 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | #481 |
| commutator, Frattini, cosocle | C2×C8 | C23×C29 |
| prime radical | C23×C29 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C2×M16×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#365 | C2 | semidirect |
| 4. C29×#362 | C2 | semidirect |
| 40. #2239 | C29 | direct (N × H) |
| 51. #365 | C2×C29 | semidirect |
| 52. #362 | C2×C29 | semidirect |
| 66. C29 | #2239 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#470 | 2 |
| C29×#430 | 2 |
| C29×#365 | 2 |
| C29×#362 | 2 |
| C29×#349 | 2 |
| #2239 | 29 |