Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
642 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 199 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 |
|---|---|---|
| 2. #20275675 | C2 | semidirect |
| 4. C2×C8×#88322 | C2 | semidirect |
| 5. C53×#1844 | C2 | semidirect |
| 10. #16810996 | C4 | semidirect |
| 73. C2×#88322 | SD16 | semidirect |
| 101. C8×C53 | #102 | semidirect |
| 123. #1844 | D53 | semidirect |
| 143. C53 | #9820 | semidirect |
| 228. C8 | #13133137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810996 | 2 |
| #20275675 | 2 |
| #20275520 | 2 |
| C2×C8×#88322 | 2 |
| C53×#1844 | 2 |
| #9820 | 53 |