Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
830 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 200 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. #20289591 | C2 | semidirect |
| 6. #16811582 | C4 | semidirect |
| 21. #13133272 | C2×C4 | semidirect |
| 118. D53 | #1295 | semidirect |
| 131. C53 | C2×#1295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811582 | 2 |
| #20289591 | 2 |
| #382×D53 | 2 |
| C2×#1295 | 53 |