Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #11719535 | C2 | semidirect |
| 3. C2×#88194 | C2 | semidirect |
| 4. C2×#88077 | C2 | semidirect |
| 5. #11718876 | C2 | semidirect |
| 6. C2×#88063 | C2 | semidirect |
| 7. #11718147 | C2 | semidirect |
| 35. C2×Q8×C13 | D4 | semidirect |
| 42. C2×D4×C13 | D4 | semidirect |
| 43. C2×D4×C13 | D4 | semidirect |
| 59. C13×M16 | D4 | semidirect |
| 63. C4⋊Dic13 | D4 | semidirect |
| 66. C4×Dic13 | D4 | semidirect |
| 111. C2×AGL(1,ℤ/8) | D13 | semidirect |
| 173. C2×Q8 | C22⋊D13 | semidirect |
| 189. C2×D4 | C22⋊D13 | semidirect |
| 190. C2×D4 | C22⋊D13 | semidirect |
| 199. M16 | C22⋊D13 | semidirect |
| 208. C13 | #2002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×AGL(1,ℤ/8) | 2 |
| #11719535 | 2 |
| C2×#88194 | 2 |
| C2×#88077 | 2 |
| #11718876 | 2 |
| C2×#88063 | 2 |
| #11718147 | 2 |
| #2002 | 13 |