Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
626 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 132 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. #20290896 | C2 | semidirect |
| 3. #20290651 | C2 | semidirect |
| 4. #20289909 | C2 | semidirect |
| 15. #16810997 | C4 | semidirect |
| 16. #16810996 | C4 | semidirect |
| 17. #16810995 | C4 | semidirect |
| 20. C53×#492 | C4 | semidirect |
| 124. C8×C53 | #102 | semidirect |
| 125. #88322 | #102 | semidirect |
| 165. #492 | #6157 | semidirect |
| 173. C53 | #9842 | semidirect |
| 278. C8 | #13133279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290896 | 2 |
| #20290843 | 2 |
| #20290651 | 2 |
| #20289909 | 2 |
| #492×D53 | 2 |
| #9842 | 53 |