Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
190 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 7. #16811555 | C4 | semidirect |
| 12. #16810457 | C4 | semidirect |
| 15. C53×M64 | C4 | semidirect |
| 89. M64 | #6157 | semidirect |
| 94. C53 | #7467 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊M64 | 2 |
| C2×C16×#6157 | 2 |
| M64×D53 | 2 |
| #7467 | 53 |