Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
686 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20275707 | C2 | semidirect |
| 3. #20273323 | C2 | semidirect |
| 4. #20273178 | C2 | semidirect |
| 5. #20273132 | C2 | semidirect |
| 6. #20273072 | C2 | semidirect |
| 7. C53×#1557 | C2 | semidirect |
| 245. #1557 | D53 | semidirect |
| 285. C53 | #8486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289253 | 2 |
| #20275707 | 2 |
| #20273323 | 2 |
| #20273178 | 2 |
| #20273132 | 2 |
| #20273072 | 2 |
| C53×#1557 | 2 |
| #8486 | 53 |