Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
476 conjugacy classes of subgroups; only the 344 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 344 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | C22×D4 |
| commutator | C4 | C23×C4×C29 |
| Frattini, cosocle | C2×C4 | C24×C29 |
| prime radical | C2×#41×C29 | C22 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×#41×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#428 | C2 | semidirect |
| 4. C29×#427 | C2 | semidirect |
| 5. C2×C29×#106 | C2 | semidirect |
| 7. C29×#131 | C4 | semidirect |
| 24. M16×C29 | C2×C4 | semidirect |
| 25. C2×C8×C29 | C2×C4 | semidirect |
| 45. #2912 | C29 | direct (N × H) |
| 56. #428 | C2×C29 | semidirect |
| 57. #427 | C2×C29 | semidirect |
| 58. C2×#106 | C2×C29 | semidirect |
| 63. #131 | C4×C29 | semidirect |
| 74. C29 | #2912 | direct (N × H) |
| 81. M16 | C2×C4×C29 | semidirect |
| 82. C2×C8 | C2×C4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#131 | 2 |
| C29×#520 | 2 |
| C29×#428 | 2 |
| C29×#427 | 2 |
| C2×C29×#106 | 2 |
| #2912 | 29 |