Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
3870 conjugacy classes of subgroups; only the 1976 normal subgroups are shown.
This group has 3870 conjugacy classes of subgroups — too many to draw. Only its 1976 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. C22×#13133284 | C2 | direct (N × H) |
| 6. C2×#13133284 | C22 | direct (N × H) |
| 14. #13133284 | C23 | direct (N × H) |
| 15. C23×Dic53 | C8 | semidirect |
| 33. C22×Dic53 | C2×C8 | semidirect |
| 43. C23×C53 | C4⋊C8 | semidirect |
| 51. C2×Dic53 | C22×C8 | semidirect |
| 59. C22×C53 | C2×C4⋊C8 | semidirect |
| 66. Dic53 | C23×C8 | semidirect |
| 72. C2×C53 | C22×C4⋊C8 | semidirect |
| 84. C53 | C23×C4⋊C8 | semidirect |
| 116. C23 | #13133284 | direct (N × H) |
| 131. C22 | C2×#13133284 | direct (N × H) |
| 141. C2 | C22×#13133284 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#88324 | 2 |
| C22×#13133284 | 2 |
| C23×C4×Dic53 | 2 |
| C23×C4⋊C8 | 53 |