Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
310 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. #11719221 | C2 | semidirect |
| 5. #11718665 | C2 | semidirect |
| 6. C13×H(3,ℤ/4) | C2 | semidirect |
| 7. #11718148 | C2 | semidirect |
| 17. C2×Dic52 | C4 | semidirect |
| 18. C2×#6095 | C4 | semidirect |
| 96. H(3,ℤ/4) | D13 | semidirect |
| 169. C13 | #1905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88163 | 2 |
| #11719221 | 2 |
| #11718667 | 2 |
| #11718666 | 2 |
| #11718665 | 2 |
| C13×H(3,ℤ/4) | 2 |
| #11718148 | 2 |
| #1905 | 13 |