Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
162 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 65 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. C4×C13×Q16 | C2 | semidirect |
| 4. #11718156 | C2 | semidirect |
| 6. #11718082 | C2 | semidirect |
| 7. C4×#6090 | C2 | semidirect |
| 15. #88068 | C4 | direct (N × H) |
| 24. C13×Q16 | C2×C4 | semidirect |
| 36. #6090 | C2×C4 | semidirect |
| 54. C4×Q16 | D13 | semidirect |
| 67. C4×C13 | SD32 | semidirect |
| 91. Q16 | C4×D13 | semidirect |
| 104. C13 | C4×SD32 | semidirect |
| 128. C4 | #88068 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×Q16 | 2 |
| C2×#88068 | 2 |
| C4×D104 | 2 |
| #11718156 | 2 |
| #11718083 | 2 |
| #11718082 | 2 |
| C4×#6090 | 2 |
| C4×SD32 | 13 |