Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
202 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #20272910 | C2 | semidirect |
| 4. C4×#13133123 | C2 | semidirect |
| 5. C4×C32×C53 | C2 | semidirect |
| 58. C4×D53 | C32 | semidirect |
| 80. C4×C32 | D53 | semidirect |
| 94. C53 | #13639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C16×D53 | 2 |
| #20272910 | 2 |
| #20272852 | 2 |
| C4×#13133123 | 2 |
| C4×C32×C53 | 2 |
| #13639 | 53 |