Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
436 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 179. C53 | #13415 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811001 | 2 |
| C2×#16810440 | 2 |
| C2×#16810439 | 2 |
| #20276434 | 2 |
| #20275464 | 2 |
| #20272796 | 2 |
| C53×#2141 | 2 |
| #13415 | 53 |