Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
336 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 85 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×C13×#104 | C2 | semidirect |
| 3. C2×#88077 | C2 | semidirect |
| 4. C2×#88065 | C2 | semidirect |
| 5. M16×Dic13 | C2 | semidirect |
| 6. C4×#6101 | C2 | semidirect |
| 7. C2×#88045 | C2 | semidirect |
| 12. #88201 | C4 | semidirect |
| 13. #88198 | C4 | semidirect |
| 14. #88194 | C4 | semidirect |
| 17. #88190 | C4 | semidirect |
| 55. C13×M16 | D4 | semidirect |
| 73. #6099 | D4 | semidirect |
| 123. C2×#104 | D13 | semidirect |
| 148. Dic13 | #104 | semidirect |
| 205. M16 | C22⋊D13 | semidirect |
| 223. C13 | #1980 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11719537 | 2 |
| C2×C13×#104 | 2 |
| C2×#88077 | 2 |
| C2×#88065 | 2 |
| M16×Dic13 | 2 |
| C4×#6101 | 2 |
| C2×#88045 | 2 |
| #1980 | 13 |