Finite Group DatabasebetaFinite Group DatabasebetaOrder 16380.
112 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 112 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 |
|---|---|---|
| 2. C3⋊(C7⋊#63118) | C3 | direct (N × H) |
| 4. C32×C5×C7×C13 | C4 | semidirect |
| 13. C3×C5×C7×C13 | Dic3 | semidirect |
| 14. C3×C5×C7×C13 | C3×C4 | semidirect |
| 20. C32×C7×C13 | Dic5 | semidirect |
| 24. C32×C5×C13 | Dic7 | semidirect |
| 29. C5×C7×C13 | C3×Dic3 | semidirect |
| 36. C32×C5×C7 | #261 | semidirect |
| 38. C3×C7×C13 | C3×Dic5 | semidirect |
| 39. C3×C7×C13 | Dic15 | semidirect |
| 47. C3×C5×C13 | C3×Dic7 | semidirect |
| 48. C3×C5×C13 | Dic21 | semidirect |
| 56. C32×C13 | Dic35 | semidirect |
| 58. C3×C5×C7 | C3×#261 | semidirect |
| 59. C3×C5×C7 | C3⋊#261 | semidirect |
| 60. C7×C13 | C3×Dic15 | semidirect |
| 68. C5×C13 | C3×Dic21 | semidirect |
| 69. C32×C7 | #63118 | semidirect |
| 73. C32×C5 | C7⋊#261 | semidirect |
| 78. C3×C13 | C3×Dic35 | semidirect |
| 79. C3×C13 | Dic105 | semidirect |
| 81. C5×C7 | C3×C3⋊#261 | semidirect |
| 88. C3×C7 | C3×#63118 | semidirect |
| 89. C3×C7 | C3⋊#63118 | semidirect |
| 93. C3×C5 | C3×C7⋊#261 | semidirect |
| 94. C3×C5 | C3⋊(C7⋊#261) | semidirect |
| 96. C13 | C3×Dic105 | semidirect |
| 100. C32 | C7⋊#63118 | semidirect |
| 101. C7 | C3×C3⋊#63118 | semidirect |
| 105. C5 | C3×C3⋊(C7⋊#261) | semidirect |
| 108. C3 | C3×C7⋊#63118 | semidirect |
| 109. C3 | C3⋊(C7⋊#63118) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5×C7×D13 | 2 |
| C3⋊(C7⋊#63118) | 3 |
| C3×C7⋊#63118 | 3 |
| C3×C3⋊(C7⋊#261) | 5 |
| C3×C3⋊#63118 | 7 |
| C3×Dic105 | 13 |