Finite Group DatabasebetaFinite Group DatabasebetaOrder 33300.
132 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 36 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 | C32×C25×C37 | C22 |
| Frattini | C5 | D15×D111 |
| socle | C32×C5×C37 | C2×D5 |
| LCS | G ▷ C32×C25×C37 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊D2775 | C2 | semidirect |
| 2. C3×C37×D75 | C2 | semidirect |
| 3. C3×C25×D111 | C2 | semidirect |
| 6. C32×C25×C37 | C22 | semidirect |
| 11. C37×D75 | D3 | semidirect |
| 12. C25×D111 | D3 | semidirect |
| 20. C3×C25×C37 | C2×D3 | semidirect |
| 21. C3×C25×C37 | C2×D3 | semidirect |
| 36. C25×C37 | D32 | semidirect |
| 40. C3×D111 | D25 | semidirect |
| 46. C3×D75 | D37 | semidirect |
| 53. C32×C37 | C2×D25 | semidirect |
| 56. C32×C25 | C2×D37 | semidirect |
| 61. D111 | D75 | direct (N × H) |
| 70. D75 | D111 | direct (N × H) |
| 75. C3×C37 | D3×D25 | semidirect |
| 76. C3×C37 | C2×D75 | semidirect |
| 82. C3×C25 | D3×D37 | semidirect |
| 83. C3×C25 | C2×D111 | semidirect |
| 93. C37 | D3×D75 | semidirect |
| 102. C25 | D3×D111 | semidirect |
| 115. C32 | D25×D37 | semidirect |
| 126. C3 | D37×D75 | semidirect |
| 127. C3 | D25×D111 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D2775 | 2 |
| C3×C37×D75 | 2 |
| C3×C25×D111 | 2 |
| D25×D111 | 3 |
| D37×D75 | 3 |
| D15×D111 | 5 |
| D3×D75 | 37 |