Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 73 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. C2×#88038 | C2 | semidirect |
| 3. C4×C13×C16 | C2 | semidirect |
| 4. #11718099 | C2 | semidirect |
| 5. C4⋊#6090 | C2 | semidirect |
| 26. C13×C16 | D4 | semidirect |
| 45. C4×C16 | D13 | semidirect |
| 51. C4×C13 | M32 | semidirect |
| 80. C16 | D52 | semidirect |
| 81. C13 | #2169 | semidirect |
| 100. C4 | #88038 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88038 | 2 |
| C8×D52 | 2 |
| C4×C13×C16 | 2 |
| #11718099 | 2 |
| C4⋊#6090 | 2 |
| #2169 | 13 |