Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20287817 | C2 | semidirect |
| 3. #20276452 | C2 | semidirect |
| 4. #20276450 | C2 | semidirect |
| 5. #20274758 | C2 | semidirect |
| 6. #20272822 | C2 | semidirect |
| 7. C53×#1386 | C2 | semidirect |
| 15. #16810882 | C4 | semidirect |
| 16. #16810877 | C4 | semidirect |
| 50. #13133157 | D4 | semidirect |
| 63. M32×C53 | D4 | semidirect |
| 182. #1386 | D53 | semidirect |
| 208. C53 | #13077 | semidirect |
| 238. M32 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287817 | 2 |
| #20284378 | 2 |
| #20276452 | 2 |
| #20276450 | 2 |
| #20274758 | 2 |
| #20272822 | 2 |
| C53×#1386 | 2 |
| #13077 | 53 |