Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
204 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×#16810463 | C2 | semidirect |
| 4. C4⋊#13133123 | C2 | semidirect |
| 5. #20272895 | C2 | semidirect |
| 7. C4×Q32×C53 | C2 | semidirect |
| 93. C4×Q32 | D53 | semidirect |
| 114. C53 | #13690 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810463 | 2 |
| C2×#16810460 | 2 |
| #20276976 | 2 |
| C4⋊#13133123 | 2 |
| #20272895 | 2 |
| #20272892 | 2 |
| C4×Q32×C53 | 2 |
| #13690 | 53 |