Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
766 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | #120 |
| commutator, Frattini, cosocle | C23 | C24×C29 |
| socle | C2×C29 | C2×#120 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#585 | C2 | semidirect |
| 2. C29×#525 | C2 | semidirect |
| 3. C29×#458 | C2 | semidirect |
| 4. C29×B(4,𝔽2) | C2 | semidirect |
| 5. C29×#410 | C2 | semidirect |
| 11. C23×C4×C29 | C22 | semidirect |
| 12. C29×#123 | C22 | semidirect |
| 15. C29×#120 | C22 | semidirect |
| 17. C29×#117 | C22 | semidirect |
| 18. C29×#99 | C22 | semidirect |
| 26. C2×Q8×C29 | D4 | semidirect |
| 30. C2×D4×C29 | D4 | semidirect |
| 35. C22×C4×C29 | D4 | semidirect |
| 65. #3025 | C29 | direct (N × H) |
| 79. #585 | C2×C29 | semidirect |
| 80. #525 | C2×C29 | semidirect |
| 81. #458 | C2×C29 | semidirect |
| 82. B(4,𝔽2) | C2×C29 | semidirect |
| 83. #410 | C2×C29 | semidirect |
| 93. C23×C4 | C22×C29 | semidirect |
| 94. #123 | C22×C29 | semidirect |
| 97. #120 | C22×C29 | semidirect |
| 99. #117 | C22×C29 | semidirect |
| 100. #99 | C22×C29 | semidirect |
| 101. C29 | #3025 | direct (N × H) |
| 109. C2×Q8 | D4×C29 | semidirect |
| 113. C2×D4 | D4×C29 | semidirect |
| 118. C22×C4 | D4×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#585 | 2 |
| C29×#525 | 2 |
| C29×#458 | 2 |
| C29×B(4,𝔽2) | 2 |
| C29×#410 | 2 |
| #3025 | 29 |