Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
580 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 580 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 |
|---|---|---|
| 3. #20274996 | C2 | semidirect |
| 4. #20272834 | C2 | semidirect |
| 13. #16810416 | C4 | semidirect |
| 29. #13133132 | C2×C4 | semidirect |
| 59. C2×D4×C53 | C4⋊C4 | semidirect |
| 82. C42×C53 | C4⋊C4 | semidirect |
| 181. C53 | #12966 | semidirect |
| 221. C2×D4 | #11719919 | semidirect |
| 251. C42 | #11719919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277892 | 2 |
| C2×#16810416 | 2 |
| #20274996 | 2 |
| #20272834 | 2 |
| C53×#1887 | 2 |
| #12966 | 53 |