Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
656 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 1. C22×#6095 | C2 | semidirect |
| 3. C2×#88123 | C2 | semidirect |
| 4. C2×C4×C8×C13 | C2 | semidirect |
| 5. #11718354 | C2 | direct (N × H) |
| 13. C2×#6095 | C22 | semidirect |
| 17. #88123 | C22 | semidirect |
| 18. C4×C8×C13 | C22 | semidirect |
| 31. C2×C8×C13 | D4 | semidirect |
| 42. C2×C4×C13 | SD16 | semidirect |
| 54. C8×C13 | C2×D4 | semidirect |
| 59. C2×C4×C8 | D13 | semidirect |
| 67. C4×C13 | C2×SD16 | semidirect |
| 82. C4×C8 | C2×D13 | semidirect |
| 83. C2×C13 | #492 | semidirect |
| 100. C2×C8 | D52 | semidirect |
| 105. C13 | C2×#492 | semidirect |
| 117. C2×C4 | #6095 | semidirect |
| 122. C8 | C2×D52 | semidirect |
| 131. C4 | C2×#6095 | semidirect |
| 134. C2 | #11718354 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6095 | 2 |
| C2×#88128 | 2 |
| C2×#88123 | 2 |
| C2×C4×C8×C13 | 2 |
| #11718354 | 2 |
| C2×#492 | 13 |