Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
220 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 67 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×#16810460 | C2 | semidirect |
| 3. C4⋊#13133123 | C2 | semidirect |
| 4. #20272892 | C2 | semidirect |
| 5. C4×Q32×C53 | C2 | semidirect |
| 26. Q32×C53 | D4 | semidirect |
| 73. C4×C53 | SD64 | semidirect |
| 78. C4×Q32 | D53 | semidirect |
| 95. C53 | #13686 | semidirect |
| 102. Q32 | D212 | semidirect |
| 152. C4 | #16810460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810460 | 2 |
| #20276965 | 2 |
| C4⋊#13133123 | 2 |
| #20272892 | 2 |
| C4×Q32×C53 | 2 |
| #13686 | 53 |