Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
942 conjugacy classes of subgroups; only the 600 normal subgroups are shown.
This group has 942 conjugacy classes of subgroups — too many to draw. Only its 600 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. C2×#16811511 | C2 | direct (N × H) |
| 4. C22×#11719910 | C4 | semidirect |
| 6. #16811511 | C22 | direct (N × H) |
| 12. C2×#11719910 | C2×C4 | semidirect |
| 40. #11719910 | C22×C4 | semidirect |
| 55. C22×C53 | #346 | semidirect |
| 66. C2×C53 | C2×#346 | semidirect |
| 77. C53 | C22×#346 | semidirect |
| 120. C22 | #16811511 | direct (N × H) |
| 128. C2 | C2×#16811511 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11719910 | 2 |
| C2×#16811511 | 2 |
| C22×C4×#88322 | 2 |
| C22×#346 | 53 |