Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 626 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. #20283738 | C2 | semidirect |
| 3. #20274704 | C2 | semidirect |
| 4. #20273141 | C2 | semidirect |
| 5. #20273139 | C2 | semidirect |
| 6. #20272573 | C2 | semidirect |
| 7. C53×#1286 | C2 | semidirect |
| 56. C4×#88322 | D4 | semidirect |
| 65. C4×C8×C53 | D4 | semidirect |
| 209. #1286 | D53 | semidirect |
| 236. C53 | #9485 | semidirect |
| 274. C4×C8 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283738 | 2 |
| #20279617 | 2 |
| #20274704 | 2 |
| #20273141 | 2 |
| #20273139 | 2 |
| #20272573 | 2 |
| C53×#1286 | 2 |
| #9485 | 53 |