Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
652 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20272744 | C2 | direct (N × H) |
| 172. C2×C53 | #1354 | semidirect |
| 191. C53 | C2×#1354 | semidirect |
| 339. C2 | #20272744 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810543 | 2 |
| C2×#16810349 | 2 |
| #20272744 | 2 |
| C2×C53×#343 | 2 |
| C2×#1354 | 53 |