Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
374 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 148 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×#11719908 | C4 | semidirect |
| 11. C16×Dic53 | C4 | semidirect |
| 12. C4×C16×C53 | C4 | semidirect |
| 45. C16×C53 | C4⋊C4 | semidirect |
| 46. #11719908 | C4⋊C4 | semidirect |
| 69. C4×C53 | #367 | semidirect |
| 72. Dic53 | #367 | semidirect |
| 90. C4×C16 | #6157 | semidirect |
| 91. C53 | #12906 | semidirect |
| 125. C16 | C4⋊#6157 | semidirect |
| 150. C4 | #16811550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811550 | 2 |
| #20290651 | 2 |
| C4×C16×D53 | 2 |
| #12906 | 53 |