Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
676 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 676 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. #20275696 | C2 | semidirect |
| 3. #20273446 | C2 | semidirect |
| 5. #20273352 | C2 | semidirect |
| 6. #20273226 | C2 | semidirect |
| 12. #16811343 | C4 | semidirect |
| 14. D4×Dic106 | C4 | semidirect |
| 239. C53 | #8496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289129 | 2 |
| #20275696 | 2 |
| #20273446 | 2 |
| #20273437 | 2 |
| #20273352 | 2 |
| #20273226 | 2 |
| C53×#1505 | 2 |
| #8496 | 53 |