Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
492 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 157 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×C13×Q16 | C2 | semidirect |
| 4. C2×#88075 | C2 | semidirect |
| 5. #11718850 | C2 | direct (N × H) |
| 6. C2×#88057 | C2 | semidirect |
| 10. C2×C13×Q16 | C22 | semidirect |
| 20. #88075 | C22 | semidirect |
| 21. #88057 | C22 | semidirect |
| 68. C22×Q16 | D13 | semidirect |
| 89. C2×Q16 | C2×D13 | semidirect |
| 101. C2×C13 | #470 | semidirect |
| 128. C13 | C2×#470 | semidirect |
| 164. C2 | #11718850 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×Q16 | 2 |
| C2×#88200 | 2 |
| C22×#6094 | 2 |
| C2×#88075 | 2 |
| #11718850 | 2 |
| C2×#88057 | 2 |
| C2×#470 | 13 |