Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
578 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 176 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 |
|---|---|---|
| 21. #16811026 | C4 | semidirect |
| 22. #16811023 | C4 | semidirect |
| 23. #16811021 | C4 | semidirect |
| 26. C53×#498 | C4 | semidirect |
| 132. #498 | #6157 | semidirect |
| 147. C53 | #22258 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291508 | 2 |
| #20290903 | 2 |
| #20290782 | 2 |
| #20290781 | 2 |
| #20290640 | 2 |
| #20290433 | 2 |
| #20285224 | 2 |
| #22258 | 53 |