Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
140 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 34 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 |
|---|---|---|
| 8. #16810451 | C4 | semidirect |
| 10. C2×Q32×C53 | C4 | semidirect |
| 69. C2×Q32 | #6157 | semidirect |
| 76. C53 | #7423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289831 | 2 |
| #20289783 | 2 |
| #20276820 | 2 |
| #7423 | 53 |