Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 3. #20290659 | C2 | semidirect |
| 4. #20289558 | C2 | semidirect |
| 49. #13133132 | C8 | semidirect |
| 94. C22⋊Dic53 | C2×C8 | semidirect |
| 106. C23×C53 | C4⋊C8 | semidirect |
| 119. C2×C4×C53 | C4⋊C8 | semidirect |
| 199. C53 | #8851 | semidirect |
| 284. C23 | #13133284 | semidirect |
| 316. C2×C4 | #13133284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291562 | 2 |
| #20290688 | 2 |
| #20290659 | 2 |
| #20289558 | 2 |
| #99×Dic53 | 2 |
| #8851 | 53 |