Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #20274922 | C2 | semidirect |
| 4. #20272603 | C2 | semidirect |
| 98. C23×C53 | #108 | semidirect |
| 176. C53 | #8859 | semidirect |
| 254. C23 | #13133153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283744 | 2 |
| #20275013 | 2 |
| #20274922 | 2 |
| #20272603 | 2 |
| C53×#1459 | 2 |
| #8859 | 53 |