Finite Group DatabasebetaFinite Group DatabasebetaOrder 33516.
248 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 43 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, Fitting, socle, cosocle, hypocenter | C32×C72×C19 | C22 |
| LCS | G ▷ C32×C72×C19 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C7×D399 | C2 | semidirect |
| 2. C19×C3⋊(C3⋊(C7⋊D7)) | C2 | semidirect |
| 4. C32×C72×C19 | C22 | semidirect |
| 7. C7×D399 | D3 | semidirect |
| 12. C3×C72×C19 | C2×D3 | semidirect |
| 15. C3×D399 | D7 | semidirect |
| 23. C32×C7×C19 | C2×D7 | semidirect |
| 24. C72×C19 | D32 | semidirect |
| 25. C3⋊(C3⋊(C7⋊D7)) | D19 | semidirect |
| 27. D399 | D21 | semidirect |
| 39. C32×C72 | C2×D19 | semidirect |
| 43. C3×C7×C19 | D3×D7 | semidirect |
| 44. C3×C7×C19 | C2×D21 | semidirect |
| 58. C32×C19 | D72 | semidirect |
| 60. C3×C72 | D3×D19 | semidirect |
| 62. C7×C19 | D3×D21 | semidirect |
| 77. C32×C7 | D7×D19 | semidirect |
| 79. C3×C19 | D7×D21 | semidirect |
| 80. C72 | (C3⋊D3)⋊D19 | semidirect |
| 97. C3×C7 | D19×D21 | semidirect |
| 98. C3×C7 | D21⋊D19 | semidirect |
| 99. C19 | D212 | semidirect |
| 107. C32 | (C7⋊D7)⋊D19 | semidirect |
| 109. C7 | D57⋊D21 | semidirect |
| 116. C3 | D133⋊D21 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×D399 | 2 |
| C19×C3⋊(C3⋊(C7⋊D7)) | 2 |
| D133⋊D21 | 3 |
| D57⋊D21 | 7 |
| D212 | 19 |