Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
640 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20285866 | C2 | semidirect |
| 4. #20275691 | C2 | semidirect |
| 6. #20272547 | C2 | semidirect |
| 7. C53×#1549 | C2 | semidirect |
| 177. #1549 | D53 | semidirect |
| 206. C53 | #10292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285866 | 2 |
| #20285658 | 2 |
| #20283073 | 2 |
| #20275691 | 2 |
| #20273384 | 2 |
| #20272547 | 2 |
| C53×#1549 | 2 |
| #10292 | 53 |