Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
402 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 104 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. C4×#13133292 | C2 | semidirect |
| 2. D53⋊#334 | C2 | semidirect |
| 3. #20289675 | C2 | semidirect |
| 4. #20289674 | C2 | semidirect |
| 30. #13133240 | C8 | semidirect |
| 71. Q16×C53 | C2×C8 | semidirect |
| 92. D424 | C2×C8 | semidirect |
| 171. C53 | #11598 | semidirect |
| 218. Q16 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133292 | 2 |
| D53⋊#334 | 2 |
| #20289675 | 2 |
| #20289674 | 2 |
| C4×#13133240 | 2 |
| #11598 | 53 |