Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
6374 conjugacy classes of subgroups; only the 3275 normal subgroups are shown.
This group has 6374 conjugacy classes of subgroups — too many to draw. Only its 3275 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. C2×C53⋊#564 | C2 | semidirect |
| 2. #564×D53 | C2 | direct (N × H) |
| 4. C2×C53×#564 | C2 | semidirect |
| 5. C53⋊#564 | C22 | semidirect |
| 12. C53×#564 | C22 | semidirect |
| 47. C2×D53 | #564 | direct (N × H) |
| 53. C2×#564 | D53 | direct (N × H) |
| 55. C2×C53 | C2×#564 | semidirect |
| 57. D53 | C2×#564 | direct (N × H) |
| 59. #564 | C2×D53 | direct (N × H) |
| 67. C53 | C22×#564 | semidirect |
| 105. C2 | #564×D53 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C53⋊#564 | 2 |
| #564×D53 | 2 |
| C2×#125×D53 | 2 |
| C2×C53×#564 | 2 |
| C22×#564 | 53 |