Finite Group DatabasebetaFinite Group DatabasebetaOrder 27300.
104 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C3×C52×C7×C13 | C4 | semidirect |
| 7. C3⋊#13049936 | C7 | direct (N × H) |
| 10. C52×C7×C13 | Dic3 | semidirect |
| 16. C3×C5×C7×C13 | Dic5 | semidirect |
| 17. C3×C5×C7×C13 | AGL(1,𝔽5) | semidirect |
| 21. C3×C52×C13 | C4×C7 | semidirect |
| 29. C3×C52×C7 | Dic13 | semidirect |
| 31. C5×C7×C13 | Dic15 | semidirect |
| 32. C5×C7×C13 | ΓL(1,𝔽16) | semidirect |
| 39. C52×C13 | C7×Dic3 | semidirect |
| 41. C3×C7×C13 | #1042 | semidirect |
| 47. C3×C5×C13 | C7×Dic5 | semidirect |
| 48. C3×C5×C13 | C7×AGL(1,𝔽5) | semidirect |
| 50. C52×C7 | Dic39 | semidirect |
| 58. C3×C5×C7 | Dic65 | semidirect |
| 59. C3×C5×C7 | #63120 | semidirect |
| 61. C7×C13 | C3⋊#1042 | semidirect |
| 64. C3×C52 | C7×Dic13 | semidirect |
| 68. C5×C13 | C7×Dic15 | semidirect |
| 69. C5×C13 | C7×ΓL(1,𝔽16) | semidirect |
| 75. C3×C13 | C7×#1042 | semidirect |
| 77. C5×C7 | Dic195 | semidirect |
| 78. C5×C7 | C3⋊#63120 | semidirect |
| 83. C52 | C7×Dic39 | semidirect |
| 84. C3×C7 | #13049936 | semidirect |
| 88. C3×C5 | C7×Dic65 | semidirect |
| 89. C3×C5 | C7×#63120 | semidirect |
| 91. C13 | C7×C3⋊#1042 | semidirect |
| 95. C7 | C3⋊#13049936 | direct (N × H) |
| 98. C5 | C7×Dic195 | semidirect |
| 99. C5 | C7×C3⋊#63120 | semidirect |
| 101. C3 | C7×#13049936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5×C7×D5×C13 | 2 |
| C7×#13049936 | 3 |
| C7×C3⋊#63120 | 5 |
| C7×Dic195 | 5 |
| C3⋊#13049936 | 7 |
| C7×C3⋊#1042 | 13 |