Finite Group DatabasebetaFinite Group DatabasebetaOrder 23100.
120 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 120 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 | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C7×C11×C25 | C22 |
| Frattini | C5 | D21⋊D55 |
| socle | C3×C5×C7×C11 | C2×D5 |
| LCS | G ▷ C3×C7×C11×C25 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×D825 | C2 | semidirect |
| 2. C11×C25×D21 | C2 | semidirect |
| 3. C3×D1925 | C2 | semidirect |
| 5. C3×C7×C11×C25 | C22 | semidirect |
| 7. D1925 | D3 | semidirect |
| 15. C7×C11×C25 | C2×D3 | semidirect |
| 16. D825 | D7 | semidirect |
| 23. C25×D21 | D11 | semidirect |
| 26. C3×C11×C25 | C2×D7 | semidirect |
| 35. C3×C7×C25 | C2×D11 | semidirect |
| 36. C11×D21 | D25 | semidirect |
| 49. C11×C25 | D3×D7 | semidirect |
| 50. C3×C7×C11 | C2×D25 | semidirect |
| 55. C7×C25 | D3×D11 | semidirect |
| 71. C7×C11 | D3×D25 | semidirect |
| 72. C3×C25 | D7×D11 | semidirect |
| 85. D21 | D275 | semidirect |
| 89. C3×C11 | D7×D25 | semidirect |
| 94. C25 | D21⋊D11 | semidirect |
| 98. C3×C7 | C2×D275 | semidirect |
| 105. C11 | D21⋊D25 | semidirect |
| 109. C7 | D3×D275 | semidirect |
| 115. C3 | D7×D275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×D825 | 2 |
| C11×C25×D21 | 2 |
| C3×D1925 | 2 |
| D7×D275 | 3 |
| D21⋊D55 | 5 |
| D3×D275 | 7 |
| D21⋊D25 | 11 |