Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
800 conjugacy classes of subgroups; only the 340 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 340 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 | C22×C22⋊C4 |
| commutator | C22 | C23×C4×C29 |
| Frattini, cosocle | C23 | C24×C29 |
| prime radical | C2×C29×H(5,𝔽2) | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C22×D4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#518 | C2 | semidirect |
| 3. C29×#410 | C2 | semidirect |
| 4. C2×C29×#99 | C2 | semidirect |
| 6. C2×#41×C29 | C4 | semidirect |
| 8. C22×D4×C29 | C4 | semidirect |
| 12. C29×#117 | C22 | semidirect |
| 13. C2×C22⋊C4×C29 | C22 | semidirect |
| 14. C29×#99 | C22 | semidirect |
| 15. C24×C29 | C2×C4 | semidirect |
| 19. C2×Q8×C29 | C2×C4 | semidirect |
| 23. C2×D4×C29 | C2×C4 | semidirect |
| 24. C2×D4×C29 | C2×C4 | semidirect |
| 28. C22×C4×C29 | C2×C4 | semidirect |
| 29. C22×C4×C29 | C2×C4 | semidirect |
| 54. #2883 | C29 | direct (N × H) |
| 68. #518 | C2×C29 | semidirect |
| 69. #410 | C2×C29 | semidirect |
| 70. C2×#99 | C2×C29 | semidirect |
| 77. C2×#41 | C4×C29 | semidirect |
| 79. C22×D4 | C4×C29 | semidirect |
| 83. #117 | C22×C29 | semidirect |
| 84. C2×C22⋊C4 | C22×C29 | semidirect |
| 85. #99 | C22×C29 | semidirect |
| 86. C29 | #2883 | direct (N × H) |
| 87. C24 | C2×C4×C29 | semidirect |
| 91. C2×Q8 | C2×C4×C29 | semidirect |
| 95. C2×D4 | C2×C4×C29 | semidirect |
| 96. C2×D4 | C2×C4×C29 | semidirect |
| 100. C22×C4 | C2×C4×C29 | semidirect |
| 101. C22×C4 | 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×H(5,𝔽2) | 2 |
| C29×#518 | 2 |
| C29×#410 | 2 |
| C2×C29×#99 | 2 |
| #2883 | 29 |