Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
160 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 80 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 | C2×D8 |
| commutator | C8 | C22×C4×C29 |
| Frattini, cosocle | C2×C8 | C23×C29 |
| prime radical | C2×D8×C29 | C22 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C42×C29 ◁ C4×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×Q16×C29 | C2 | semidirect |
| 4. C29×#366 | C2 | semidirect |
| 5. C29×#358 | C2 | semidirect |
| 7. C29×#346 | C2 | semidirect |
| 12. C29×SD32 | C4 | semidirect |
| 24. Q16×C29 | C2×C4 | semidirect |
| 36. C16×C29 | C2×C4 | semidirect |
| 52. #2175 | C29 | direct (N × H) |
| 65. C4×Q16 | C2×C29 | semidirect |
| 67. #366 | C2×C29 | semidirect |
| 68. #358 | C2×C29 | semidirect |
| 70. #346 | C2×C29 | semidirect |
| 79. SD32 | C4×C29 | semidirect |
| 87. C29 | #2175 | direct (N × H) |
| 92. Q16 | C2×C4×C29 | semidirect |
| 104. C16 | 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×SD32 | 2 |
| C4×Q16×C29 | 2 |
| C4×D8×C29 | 2 |
| C29×#366 | 2 |
| C29×#358 | 2 |
| C29×#357 | 2 |
| C29×#346 | 2 |
| #2175 | 29 |