Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
354 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 1. #20276972 | C2 | semidirect |
| 3. C8×#11719908 | C2 | semidirect |
| 4. C53×#1713 | C2 | semidirect |
| 32. #11719908 | D8 | semidirect |
| 40. C8×C53 | SD32 | semidirect |
| 50. #1713 | D53 | semidirect |
| 63. C53 | #12517 | semidirect |
| 92. C8 | #13133160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276972 | 2 |
| #20274330 | 2 |
| C8×#11719908 | 2 |
| C53×#1713 | 2 |
| #12517 | 53 |