Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
446 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 1. #20291048 | C2 | semidirect |
| 3. #20290650 | C2 | semidirect |
| 4. #20289786 | C2 | semidirect |
| 15. Q16×Dic53 | C4 | semidirect |
| 18. C4×D424 | C4 | semidirect |
| 19. #16810705 | C4 | semidirect |
| 23. C4×Q16×C53 | C4 | semidirect |
| 83. Q16×C53 | C4⋊C4 | semidirect |
| 105. D424 | C4⋊C4 | semidirect |
| 162. C4×C53 | #360 | semidirect |
| 167. Dic53 | #360 | semidirect |
| 185. C4×Q16 | #6157 | semidirect |
| 199. C53 | #12816 | semidirect |
| 255. Q16 | C4⋊#6157 | semidirect |
| 342. C4 | #16811540 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291048 | 2 |
| C2×#16811540 | 2 |
| #20290650 | 2 |
| #20289786 | 2 |
| C4×#13133240 | 2 |
| #12816 | 53 |