Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
708 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 162 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×#13133284 | C2 | semidirect |
| 3. #20289593 | C2 | semidirect |
| 8. #16811481 | C4 | direct (N × H) |
| 20. #13133284 | C2×C4 | semidirect |
| 147. C4×C53 | #331 | semidirect |
| 176. C53 | C4×#331 | semidirect |
| 309. C4 | #16811481 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133284 | 2 |
| C2×#16811481 | 2 |
| #20289593 | 2 |
| C4×#13133213 | 2 |
| C4×#331 | 53 |