Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
220 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. #20273624 | C2 | semidirect |
| 4. #20272780 | C2 | semidirect |
| 6. #20272635 | C2 | semidirect |
| 7. C53×#1334 | C2 | semidirect |
| 103. #1334 | D53 | semidirect |
| 125. C53 | #12077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276577 | 2 |
| #20273624 | 2 |
| #20273538 | 2 |
| #20272780 | 2 |
| #20272683 | 2 |
| #20272635 | 2 |
| C53×#1334 | 2 |
| #12077 | 53 |