Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#88205 | C2 | semidirect |
| 3. C2×#88190 | C2 | semidirect |
| 4. #11718903 | C2 | direct (N × H) |
| 5. C2×#88077 | C2 | semidirect |
| 6. C2×#88073 | C2 | semidirect |
| 15. C22×Dic26 | C22 | semidirect |
| 18. #88205 | C22 | semidirect |
| 21. #88190 | C22 | semidirect |
| 23. C2×C4×Dic13 | C22 | semidirect |
| 24. C2×#6099 | C22 | semidirect |
| 25. #88077 | C22 | semidirect |
| 26. #88073 | C22 | semidirect |
| 55. C2×Dic26 | C23 | semidirect |
| 60. C4×Dic13 | C23 | semidirect |
| 62. #6099 | C23 | semidirect |
| 144. C2×C13 | #455 | semidirect |
| 183. C13 | C2×#455 | semidirect |
| 237. C2 | #11718903 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×H(5,𝔽2) | 2 |
| C2×#88205 | 2 |
| C2×#88190 | 2 |
| #11718903 | 2 |
| C2×#88077 | 2 |
| C2×#88073 | 2 |
| C2×#455 | 13 |