Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
652 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 213 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×Q8×Dic13 | C2 | semidirect |
| 4. C13×#391 | C2 | semidirect |
| 5. #11718638 | C2 | semidirect |
| 7. C42×Dic13 | C2 | semidirect |
| 8. #11718331 | C2 | semidirect |
| 9. #11718327 | C2 | semidirect |
| 15. #88201 | C4 | semidirect |
| 33. C2×Q8×C13 | C2×C4 | semidirect |
| 51. #6103 | C2×C4 | semidirect |
| 57. C4×Dic13 | C2×C4 | semidirect |
| 92. #391 | D13 | semidirect |
| 115. Dic13 | #124 | semidirect |
| 145. C2×Q8 | C4×D13 | semidirect |
| 171. C13 | C4×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88201 | 2 |
| C2×Q8×Dic13 | 2 |
| C2×#88147 | 2 |
| C13×#391 | 2 |
| #11718638 | 2 |
| #11718600 | 2 |
| C42×Dic13 | 2 |
| #11718331 | 2 |
| #11718327 | 2 |
| C4×#124 | 13 |