Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
560 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20283743 | C2 | semidirect |
| 3. C4×#13133133 | C2 | semidirect |
| 4. #20273313 | C2 | semidirect |
| 5. #20272581 | C2 | semidirect |
| 6. #20272580 | C2 | semidirect |
| 7. C53×#1527 | C2 | semidirect |
| 56. #13133128 | D4 | semidirect |
| 77. #97×C53 | D4 | semidirect |
| 235. #1527 | D53 | semidirect |
| 269. C53 | #9187 | semidirect |
| 309. #97 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283743 | 2 |
| #20280568 | 2 |
| C4×#13133133 | 2 |
| #20273313 | 2 |
| #20272581 | 2 |
| #20272580 | 2 |
| C53×#1527 | 2 |
| #9187 | 53 |