Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
6110 conjugacy classes of subgroups; only the 744 normal subgroups are shown.
This group has 6110 conjugacy classes of subgroups — too many to draw. Only its 744 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. C22×C22⋊#88324 | C2 | semidirect |
| 2. #20290537 | C2 | direct (N × H) |
| 4. C23×#88324 | C22 | semidirect |
| 6. C2×C22⋊#88324 | C22 | semidirect |
| 14. C22×#88324 | C23 | semidirect |
| 30. C25×C53 | C8 | semidirect |
| 42. C24×C53 | C2×C8 | semidirect |
| 74. C23×C53 | C22⋊C8 | semidirect |
| 101. C22×C53 | C2×C22⋊C8 | semidirect |
| 113. C2×C53 | #1779 | semidirect |
| 126. C53 | C2×#1779 | semidirect |
| 129. C25 | #88324 | semidirect |
| 155. C24 | C2×#88324 | semidirect |
| 188. C23 | C22⋊#88324 | semidirect |
| 214. C22 | C2×C22⋊#88324 | semidirect |
| 223. C2 | #20290537 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊#88324 | 2 |
| #20290537 | 2 |
| C25×Dic53 | 2 |
| C2×#1779 | 53 |