Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
324 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 10. C4×Q8×C13 | C4 | semidirect |
| 11. Q8×Dic13 | C4 | semidirect |
| 15. #88141 | C4 | semidirect |
| 19. C4×Dic26 | C4 | semidirect |
| 20. #88117 | C4 | semidirect |
| 62. Q8×C13 | C42 | semidirect |
| 83. Dic26 | C42 | semidirect |
| 114. C4×Q8 | #261 | semidirect |
| 162. C13 | #1763 | semidirect |
| 168. Q8 | C4×#261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D13 | 2 |
| C2×#88117 | 2 |
| C4×C4⋊#261 | 2 |
| #11719047 | 2 |
| #11718246 | 2 |
| #1763 | 13 |