Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
510 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 312 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 |
|---|---|---|
| 5. #16811511 | C4 | direct (N × H) |
| 6. C4×#11719910 | C4 | semidirect |
| 39. #11719910 | C42 | semidirect |
| 57. C4×C53 | #346 | semidirect |
| 75. C53 | C4×#346 | semidirect |
| 120. C4 | #16811511 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811511 | 2 |
| C2×C4×#11719910 | 2 |
| C42×#88322 | 2 |
| C4×#346 | 53 |