Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2878 conjugacy classes of subgroups; only the 440 normal subgroups are shown.
This group has 2878 conjugacy classes of subgroups — too many to draw. Only its 440 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. C2×#16811467 | C2 | direct (N × H) |
| 6. C2×C22⋊#88324 | C22 | semidirect |
| 7. #16811467 | C22 | direct (N × H) |
| 18. C22⋊#88324 | C23 | semidirect |
| 24. C24×D53 | C8 | semidirect |
| 62. C23×D53 | C2×C8 | semidirect |
| 113. C22×D53 | C22×C8 | semidirect |
| 135. C22×C53 | #323 | semidirect |
| 159. C2×C53 | C2×#323 | semidirect |
| 175. C53 | C22×#323 | semidirect |
| 302. C22 | #16811467 | direct (N × H) |
| 317. C2 | C2×#16811467 | 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 |
| C2×#16811467 | 2 |
| C23×#11719921 | 2 |
| C22×#323 | 53 |