Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
392 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C29 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C29 |
| socle | C22×C29 | C22×D4 |
| prime radical | C29×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#533 | C2 | semidirect |
| 3. C29×#491 | C2 | semidirect |
| 4. C29×#490 | C2 | semidirect |
| 5. C29×#489 | C2 | semidirect |
| 6. C29×#416 | C2 | semidirect |
| 7. C2×C29×#97 | C2 | semidirect |
| 63. #3135 | C29 | direct (N × H) |
| 75. #533 | C2×C29 | semidirect |
| 77. #491 | C2×C29 | semidirect |
| 78. #490 | C2×C29 | semidirect |
| 79. #489 | C2×C29 | semidirect |
| 80. #416 | C2×C29 | semidirect |
| 81. C2×#97 | C2×C29 | semidirect |
| 103. C29 | #3135 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#533 | 2 |
| C29×#532 | 2 |
| C29×#491 | 2 |
| C29×#490 | 2 |
| C29×#489 | 2 |
| C29×#416 | 2 |
| C2×C29×#97 | 2 |
| #3135 | 29 |