Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
1664 conjugacy classes of subgroups; only the 850 normal subgroups are shown.
This group has 1664 conjugacy classes of subgroups — too many to draw. Only its 850 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. C2×Q8×#261 | C2 | direct (N × H) |
| 7. C22×Q8×C13 | C4 | semidirect |
| 8. C2×Q8×D13 | C4 | semidirect |
| 11. C22×Dic26 | C4 | semidirect |
| 12. Q8×#261 | C22 | direct (N × H) |
| 17. C22×#261 | Q8 | direct (N × H) |
| 20. C2×Q8×C13 | C2×C4 | semidirect |
| 23. Q8×D13 | C2×C4 | semidirect |
| 27. C2×Dic26 | C2×C4 | semidirect |
| 37. C2×#261 | C2×Q8 | direct (N × H) |
| 40. Q8×C13 | C22×C4 | semidirect |
| 45. Dic26 | C22×C4 | semidirect |
| 50. C22×C13 | C4×Q8 | semidirect |
| 52. C2×D13 | C4×Q8 | semidirect |
| 58. #261 | C22×Q8 | direct (N × H) |
| 64. C22×Q8 | #261 | direct (N × H) |
| 71. C2×C13 | C2×C4×Q8 | semidirect |
| 73. D13 | C2×C4×Q8 | semidirect |
| 80. C2×Q8 | C2×#261 | direct (N × H) |
| 91. C13 | C22×C4×Q8 | semidirect |
| 98. Q8 | C22×#261 | direct (N × H) |
| 112. C22 | Q8×#261 | direct (N × H) |
| 121. C2 | C2×Q8×#261 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D13 | 2 |
| C2×Q8×#261 | 2 |
| C22×C4⋊#261 | 2 |
| C22×C4×#261 | 2 |
| C22×C4×Q8 | 13 |