Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
376 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 2. C4×C4⋊#88322 | C2 | semidirect |
| 3. #20273490 | C2 | semidirect |
| 6. #20272611 | C2 | semidirect |
| 7. C53×#1276 | C2 | semidirect |
| 17. #16810368 | C4 | semidirect |
| 18. #16810366 | C4 | semidirect |
| 156. #1276 | D53 | semidirect |
| 178. C53 | #9577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275543 | 2 |
| C4×C4⋊#88322 | 2 |
| #20273490 | 2 |
| #20273362 | 2 |
| #20273115 | 2 |
| #20272611 | 2 |
| C53×#1276 | 2 |
| #9577 | 53 |