Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
438 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #20273248 | C2 | semidirect |
| 4. #20273079 | C2 | semidirect |
| 5. #20272624 | C2 | semidirect |
| 6. #20272591 | C2 | semidirect |
| 27. C53×#484 | C4 | semidirect |
| 28. C53×#481 | C4 | semidirect |
| 32. C53×#451 | C4 | semidirect |
| 33. C53×#448 | C4 | semidirect |
| 227. #484 | Dic53 | semidirect |
| 228. #481 | Dic53 | semidirect |
| 232. #451 | Dic53 | semidirect |
| 233. #448 | Dic53 | semidirect |
| 251. C53 | #9331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283777 | 2 |
| #20273271 | 2 |
| #20273248 | 2 |
| #20273079 | 2 |
| #20272624 | 2 |
| #20272591 | 2 |
| C53×#3196 | 2 |
| #9331 | 53 |