Finite Group DatabasebetaFinite Group DatabasebetaOrder 38220.
144 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 42 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×C5×C72×C13 | C4 | semidirect |
| 6. C3⋊(C7⋊#63121) | C7 | direct (N × H) |
| 9. C5×C72×C13 | Dic3 | semidirect |
| 15. C3×C72×C13 | AGL(1,𝔽5) | semidirect |
| 20. C3×C5×C7×C13 | Dic7 | semidirect |
| 21. C3×C5×C7×C13 | C4×C7 | semidirect |
| 30. C3×C5×C72 | #261 | semidirect |
| 31. C72×C13 | ΓL(1,𝔽16) | semidirect |
| 38. C5×C7×C13 | C7×Dic3 | semidirect |
| 39. C5×C7×C13 | Dic21 | semidirect |
| 47. C3×C7×C13 | C7×AGL(1,𝔽5) | semidirect |
| 48. C3×C7×C13 | C7⋊AGL(1,𝔽5) | semidirect |
| 50. C5×C72 | C3⋊#261 | semidirect |
| 55. C3×C5×C13 | C7×Dic7 | semidirect |
| 60. C3×C72 | #63121 | semidirect |
| 65. C3×C5×C7 | C7×#261 | semidirect |
| 66. C3×C5×C7 | C7⋊#261 | semidirect |
| 69. C7×C13 | C7×ΓL(1,𝔽16) | semidirect |
| 70. C7×C13 | C3⋊(C7⋊AGL(1,𝔽5)) | semidirect |
| 77. C5×C13 | C7×Dic21 | semidirect |
| 80. C72 | C3⋊#63121 | semidirect |
| 84. C3×C13 | C7×C7⋊AGL(1,𝔽5) | semidirect |
| 86. C5×C7 | C7×C3⋊#261 | semidirect |
| 87. C5×C7 | C3⋊(C7⋊#261) | semidirect |
| 93. C3×C7 | C7×#63121 | semidirect |
| 94. C3×C7 | C7⋊#63121 | semidirect |
| 96. C3×C5 | C7×C7⋊#261 | semidirect |
| 100. C13 | C7×C3⋊(C7⋊AGL(1,𝔽5)) | semidirect |
| 104. C7 | C7×C3⋊#63121 | semidirect |
| 105. C7 | C3⋊(C7⋊#63121) | direct (N × H) |
| 107. C5 | C7×C3⋊(C7⋊#261) | semidirect |
| 109. C3 | C7×C7⋊#63121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C72×D65 | 2 |
| C7×C7⋊#63121 | 3 |
| C7×C3⋊(C7⋊#261) | 5 |
| C3⋊(C7⋊#63121) | 7 |
| C7×C3⋊#63121 | 7 |
| C7×C3⋊(C7⋊AGL(1,𝔽5)) | 13 |