Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
664 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 664 conjugacy classes of subgroups — too many to draw. Only its 159 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×Q32×D53 | C2 | semidirect |
| 3. #20276968 | C2 | semidirect |
| 4. #20276807 | C2 | semidirect |
| 5. #20276765 | C2 | semidirect |
| 6. #20276650 | C2 | semidirect |
| 8. C4×Q32×C53 | C2 | semidirect |
| 52. Q32×C53 | D4 | semidirect |
| 100. D212 | Q32 | direct (N × H) |
| 115. C2×D53 | C2×Q32 | semidirect |
| 119. C4×C53 | C2×Q32 | semidirect |
| 130. C4×Q32 | D53 | semidirect |
| 156. C53 | D4×Q32 | semidirect |
| 175. Q32 | D212 | direct (N × H) |
| 248. C4 | Q32×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q32×D53 | 2 |
| Q16×D212 | 2 |
| #20276968 | 2 |
| #20276807 | 2 |
| #20276765 | 2 |
| #20276650 | 2 |
| C16×D212 | 2 |
| C4×Q32×C53 | 2 |
| D4×Q32 | 53 |