Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 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. C2×C13×C4⋊Q8 | C2 | semidirect |
| 2. C2×#88196 | C2 | semidirect |
| 4. #11718753 | C2 | semidirect |
| 5. #11718747 | C2 | semidirect |
| 6. #11718746 | C2 | semidirect |
| 7. C4×#6099 | C2 | semidirect |
| 47. #6099 | D4 | semidirect |
| 71. C2×C4⋊Q8 | D13 | semidirect |
| 84. C4×C13 | #137 | semidirect |
| 132. C13 | #3152 | semidirect |
| 161. C4 | #88196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×C4⋊Q8 | 2 |
| C2×#88196 | 2 |
| #11719182 | 2 |
| #11718753 | 2 |
| #11718747 | 2 |
| #11718746 | 2 |
| C4×#6099 | 2 |
| #3152 | 13 |