Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 134 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 |
|---|---|---|
| 9. #16811536 | C4 | direct (N × H) |
| 15. C4×Dic212 | C4 | semidirect |
| 16. Q16×Dic53 | C4 | semidirect |
| 17. #16810717 | C4 | semidirect |
| 23. C4×Q16×C53 | C4 | semidirect |
| 76. Q16×C53 | C42 | semidirect |
| 98. Dic212 | C42 | semidirect |
| 144. C4×C53 | #358 | semidirect |
| 150. Dic53 | #358 | semidirect |
| 170. C4×Q16 | #6157 | semidirect |
| 180. C53 | C4×#358 | semidirect |
| 233. Q16 | C4×#6157 | semidirect |
| 305. C4 | #16811536 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811536 | 2 |
| C4×D53⋊C16 | 2 |
| C4×#13133286 | 2 |
| #20289772 | 2 |
| C4×Q16×D53 | 2 |
| C4×#358 | 53 |