Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 124 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 | semidirect |
| 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 |
| 171. C4×Q16 | #6157 | semidirect |
| 181. C53 | #12638 | semidirect |
| 234. Q16 | C4×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811536 | 2 |
| #20290916 | 2 |
| C4×#13133286 | 2 |
| #20289772 | 2 |
| C4×Q16×D53 | 2 |
| #12638 | 53 |