Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
476 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 67 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. #20276632 | C2 | semidirect |
| 3. #20272723 | C2 | semidirect |
| 4. #20272639 | C2 | semidirect |
| 5. C53×#2001 | C2 | semidirect |
| 13. C22⋊#11719908 | C22 | semidirect |
| 14. C22×Q16×C53 | C22 | semidirect |
| 18. C53×#340 | C22 | semidirect |
| 94. C23×C53 | SD32 | semidirect |
| 153. #2001 | D53 | semidirect |
| 163. C22×Q16 | C2×D53 | semidirect |
| 175. #340 | C2×D53 | semidirect |
| 176. C53 | #12105 | semidirect |
| 256. C23 | #13133160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285466 | 2 |
| #20276632 | 2 |
| #20272723 | 2 |
| #20272639 | 2 |
| C53×#2001 | 2 |
| #12105 | 53 |