Finite Group DatabasebetaFinite Group DatabasebetaOrder 26100.
160 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C3⋊(C29⋊#3874) |
| commutator, cosocle, hypocenter | C3×C29×C52⋊C3 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C52×C29 | D3 |
| LCS | G ▷ C3×C29×C52⋊C3 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C29×C52⋊C3 | C2 | semidirect |
| 2. C3⋊(C29⋊#3874) | C2 | direct (N × H) |
| 6. C3×C29×C52⋊C3 | C22 | semidirect |
| 8. C2×C29×C52⋊C3 | D3 | semidirect |
| 9. C2×C29×C52⋊C3 | D3 | semidirect |
| 12. C2×C3×C52×C29 | D3 | semidirect |
| 14. C29×C52⋊C3 | C2×D3 | semidirect |
| 15. C29×C52⋊C3 | C2×D3 | semidirect |
| 16. C3×C52×C29 | C2×D3 | semidirect |
| 19. C2×C52×C29 | C3⋊D3 | semidirect |
| 27. C52×C29 | C2×C3⋊D3 | semidirect |
| 32. C2×C3×C52⋊C3 | D29 | semidirect |
| 47. C3×C52⋊C3 | C2×D29 | semidirect |
| 50. C2×C3×C29 | #3874 | semidirect |
| 54. C2×C3×C52 | D87 | semidirect |
| 56. C2×C52⋊C3 | D87 | semidirect |
| 57. C2×C52⋊C3 | D87 | semidirect |
| 66. C3×C29 | C2×#3874 | semidirect |
| 67. C3×C52 | C2×D87 | semidirect |
| 68. C52⋊C3 | C2×D87 | semidirect |
| 69. C52⋊C3 | C2×D87 | semidirect |
| 72. C2×C29 | C3⋊#3874 | semidirect |
| 74. C2×C52 | C3⋊D87 | semidirect |
| 81. C29 | C2×C3⋊#3874 | semidirect |
| 82. C52 | C2×C3⋊D87 | semidirect |
| 99. C2×C3 | C29⋊#3874 | semidirect |
| 108. C3 | C2×C29⋊#3874 | semidirect |
| 110. C2 | C3⋊(C29⋊#3874) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C29×C52⋊C3 | 2 |
| C3⋊(C29⋊#3874) | 2 |
| C2×C5×D435 | 3 |
| C2×C29⋊#3874 | 3 |
| C2×C3⋊D87 | 25 |
| C2×C3⋊#3874 | 29 |