Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
734 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20284716 | C2 | semidirect |
| 2. #20284715 | C2 | semidirect |
| 3. #20277994 | C2 | semidirect |
| 4. #20275546 | C2 | semidirect |
| 5. #20273139 | C2 | semidirect |
| 6. #20272543 | C2 | semidirect |
| 7. C53×#1486 | C2 | semidirect |
| 39. #13133217 | D4 | semidirect |
| 40. #13133214 | D4 | semidirect |
| 67. C4×#88322 | D4 | semidirect |
| 84. C4×C8×C53 | D4 | semidirect |
| 142. C4×Dic53 | D8 | semidirect |
| 234. #1486 | D53 | semidirect |
| 268. C53 | #10012 | semidirect |
| 318. C4×C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284716 | 2 |
| #20284715 | 2 |
| #20277994 | 2 |
| #20275546 | 2 |
| #20273139 | 2 |
| #20272543 | 2 |
| C53×#1486 | 2 |
| #10012 | 53 |