Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
166 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 166 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. C8×Q8×C13 | C2 | semidirect |
| 4. Q8⋊#1055 | C2 | semidirect |
| 6. #11718071 | C2 | semidirect |
| 7. #11718046 | C2 | semidirect |
| 44. Q8×C13 | M16 | semidirect |
| 62. C8×Q8 | D13 | semidirect |
| 118. C13 | #1588 | semidirect |
| 121. Q8 | #6094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Q8×C13 | 2 |
| C4×#6106 | 2 |
| #11718349 | 2 |
| Q8⋊#1055 | 2 |
| #11718075 | 2 |
| #11718071 | 2 |
| #11718046 | 2 |
| #1588 | 13 |