Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
354 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 152 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 |
|---|---|---|
| 6. #16811464 | C4 | semidirect |
| 7. C8×#88324 | C4 | semidirect |
| 23. #13133127 | C8 | semidirect |
| 32. #97×C53 | C8 | semidirect |
| 106. C53 | #8138 | semidirect |
| 118. #97 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289918 | 2 |
| #20289541 | 2 |
| #20289539 | 2 |
| #20274403 | 2 |
| #8138 | 53 |