Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
112 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 28 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 | AΣL(1,𝔽16) |
| commutator | C2×Q8 | C2×C4×C29 |
| Frattini, cosocle | #124 | C22×C29 |
| prime radical | C29×#454 | C2 |
| LCS | G ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C22×C29 ◁ C2×C4×C29 ◁ C29×#124 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#354 | C2 | semidirect |
| 3. C29×#329 | C2 | semidirect |
| 4. C29×2−1+4 | C4 | semidirect |
| 8. C29×#101 | C4 | semidirect |
| 40. #1404 | C29 | direct (N × H) |
| 51. #354 | C2×C29 | semidirect |
| 52. #329 | C2×C29 | semidirect |
| 57. 2−1+4 | C4×C29 | semidirect |
| 61. #101 | C4×C29 | semidirect |
| 64. C29 | #1404 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#454 | 2 |
| C29×#354 | 2 |
| C29×#329 | 2 |
| #1404 | 29 |