Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
270 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 270 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 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C23×C29 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C22×C29 ◁ C2×D4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×H(3,𝔽4) | C2 | semidirect |
| 2. C29×B(4,𝔽2) | C2 | semidirect |
| 3. C29×#455 | C2 | semidirect |
| 4. C29×#354 | C2 | semidirect |
| 5. C29×AΣL(1,𝔽16) | C2 | semidirect |
| 19. C24×C29 | D4 | semidirect |
| 23. C2×Q8×C29 | D4 | semidirect |
| 40. C22⋊C4×C29 | D4 | semidirect |
| 42. C42×C29 | D4 | semidirect |
| 67. #2199 | C29 | direct (N × H) |
| 84. H(3,𝔽4) | C2×C29 | semidirect |
| 85. B(4,𝔽2) | C2×C29 | semidirect |
| 86. #455 | C2×C29 | semidirect |
| 87. #354 | C2×C29 | semidirect |
| 88. AΣL(1,𝔽16) | C2×C29 | semidirect |
| 107. C29 | #2199 | direct (N × H) |
| 108. C24 | D4×C29 | semidirect |
| 112. C2×Q8 | D4×C29 | semidirect |
| 129. C22⋊C4 | D4×C29 | semidirect |
| 131. C42 | D4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×H(3,𝔽4) | 2 |
| C29×B(4,𝔽2) | 2 |
| C29×#455 | 2 |
| C29×#354 | 2 |
| C29×AΣL(1,𝔽16) | 2 |
| #2199 | 29 |