Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
950 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20285635 | C2 | semidirect |
| 2. #20283110 | C2 | semidirect |
| 3. #20275543 | C2 | semidirect |
| 4. #20273382 | C2 | semidirect |
| 5. C53×#1276 | C2 | semidirect |
| 26. #13133217 | D4 | semidirect |
| 34. #13133214 | D4 | semidirect |
| 44. C4⋊C8×C53 | D4 | semidirect |
| 73. C42×C53 | D8 | semidirect |
| 135. #1276 | D53 | semidirect |
| 154. C53 | #10280 | semidirect |
| 178. C4⋊C8 | D212 | semidirect |
| 214. C42 | D424 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285635 | 2 |
| #20283110 | 2 |
| #20275543 | 2 |
| #20273382 | 2 |
| C53×#1276 | 2 |
| #10280 | 53 |