Finite Group DatabasebetaFinite Group DatabasebetaOrder 15300.
160 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C17×C52⋊C3 | C22 |
| Fitting, socle | C3×C52×C17 | C2×D3 |
| LCS | G ▷ C3×C17×C52⋊C3 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊(C17⋊#3874) | C2 | semidirect |
| 2. C17×C3⋊#3874 | C2 | semidirect |
| 3. C3×D17×C52⋊C3 | C2 | semidirect |
| 8. C3×C17×C52⋊C3 | C22 | semidirect |
| 11. C3×C52×D17 | D3 | semidirect |
| 12. D17×C52⋊C3 | D3 | semidirect |
| 13. D17×C52⋊C3 | D3 | semidirect |
| 14. D17×C52⋊C3 | D3 | semidirect |
| 22. C3×C52×C17 | C2×D3 | semidirect |
| 23. C17×C52⋊C3 | C2×D3 | semidirect |
| 24. C17×C52⋊C3 | C2×D3 | semidirect |
| 25. C17×C52⋊C3 | C2×D3 | semidirect |
| 31. C52×D17 | C3⋊D3 | semidirect |
| 41. C3⋊#3874 | D17 | direct (N × H) |
| 42. C52×C17 | C2×C3⋊D3 | semidirect |
| 54. C3×C52⋊C3 | C2×D17 | semidirect |
| 85. C3×D17 | #3874 | semidirect |
| 93. C3×C52 | D3×D17 | semidirect |
| 94. C52⋊C3 | D3×D17 | semidirect |
| 95. C52⋊C3 | D3×D17 | semidirect |
| 96. C52⋊C3 | D3×D17 | semidirect |
| 103. C3×C17 | C2×#3874 | semidirect |
| 110. D17 | C3⋊#3874 | direct (N × H) |
| 117. C52 | C3⋊D3×D17 | semidirect |
| 123. C17 | C2×C3⋊#3874 | semidirect |
| 155. C3 | D17×#3874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊(C17⋊#3874) | 2 |
| C17×C3⋊#3874 | 2 |
| C3×D17×C52⋊C3 | 2 |
| C5×D15×D17 | 3 |
| D17×#3874 | 3 |
| C2×C3⋊#3874 | 17 |
| C3⋊D3×D17 | 25 |