Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
684 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 207 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×C4⋊#88322 | C2 | semidirect |
| 2. #20272536 | C2 | semidirect |
| 21. #127×C53 | C8 | semidirect |
| 131. C53 | #7569 | semidirect |
| 137. #127 | #88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊#88322 | 2 |
| #20272536 | 2 |
| C4×#127×C53 | 2 |
| #7569 | 53 |