Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
280 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. C2×#88054 | C2 | semidirect |
| 5. C2×#88043 | C2 | semidirect |
| 6. C13×#336 | C2 | semidirect |
| 7. #11718142 | C2 | semidirect |
| 98. #336 | D13 | semidirect |
| 176. C13 | #1924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88060 | 2 |
| C2×#88054 | 2 |
| C4×#6103 | 2 |
| C2×#88043 | 2 |
| C13×#336 | 2 |
| #11718142 | 2 |
| #1924 | 13 |