Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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×#16811061 | C2 | semidirect |
| 2. #20284435 | C2 | semidirect |
| 3. #20284363 | C2 | semidirect |
| 4. C2×#16810437 | C2 | semidirect |
| 5. #20276452 | C2 | semidirect |
| 6. #20272830 | C2 | semidirect |
| 7. C53×#2117 | C2 | semidirect |
| 42. C2×Dic212 | D4 | semidirect |
| 50. C2×D424 | D4 | semidirect |
| 60. #13133153 | D4 | semidirect |
| 78. M32×C53 | D4 | semidirect |
| 210. #2117 | D53 | semidirect |
| 242. C53 | #13310 | semidirect |
| 283. M32 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811061 | 2 |
| #20284435 | 2 |
| #20284363 | 2 |
| C2×#16810437 | 2 |
| #20276452 | 2 |
| #20272830 | 2 |
| C53×#2117 | 2 |
| #13310 | 53 |