Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 133 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×C4×Q8×C13 | C2 | semidirect |
| 3. #11718888 | C2 | semidirect |
| 4. #11718688 | C2 | semidirect |
| 5. #11718687 | C2 | semidirect |
| 6. #11718682 | C2 | semidirect |
| 7. #11718628 | C2 | semidirect |
| 8. #11718587 | C2 | semidirect |
| 69. Q8×C13 | #41 | semidirect |
| 92. C2×C4×Q8 | D13 | semidirect |
| 175. C13 | #3112 | semidirect |
| 181. Q8 | #6127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Q8×C13 | 2 |
| #11719182 | 2 |
| #11718888 | 2 |
| #11718688 | 2 |
| #11718687 | 2 |
| #11718682 | 2 |
| #11718628 | 2 |
| #11718587 | 2 |
| #3112 | 13 |