Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
414 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 11. #16811485 | C4 | semidirect |
| 12. C8×#88324 | C4 | semidirect |
| 90. #88324 | #106 | semidirect |
| 92. #88322 | #97 | semidirect |
| 131. C53 | #8283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290511 | 2 |
| C2×#16811485 | 2 |
| C2×C8×#88324 | 2 |
| #20289551 | 2 |
| #20274603 | 2 |
| #8283 | 53 |