Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
140 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
|---|---|---|
| 6. C2×Q32×C53 | C4 | semidirect |
| 9. C53×#367 | C4 | semidirect |
| 69. C2×Q32 | Dic53 | semidirect |
| 74. #367 | Dic53 | semidirect |
| 76. C53 | #7423 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20272855 | 2 |
| #20272817 | 2 |
| C53×#2219 | 2 |
| #7423 | 53 |