Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
230 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 51 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×#88173 | C2 | semidirect |
| 2. C2×#88068 | C2 | semidirect |
| 3. C2×D208 | C2 | semidirect |
| 4. #11718544 | C2 | semidirect |
| 5. C13×#358 | C2 | semidirect |
| 6. #11718099 | C2 | semidirect |
| 7. #11718083 | C2 | semidirect |
| 33. C13×Q16 | D4 | semidirect |
| 42. D104 | D4 | semidirect |
| 73. #358 | D13 | semidirect |
| 122. Q16 | D52 | semidirect |
| 136. C13 | #2186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88173 | 2 |
| C2×#88068 | 2 |
| C2×D208 | 2 |
| #11718544 | 2 |
| C13×#358 | 2 |
| #11718099 | 2 |
| #11718083 | 2 |
| #2186 | 13 |