Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
614 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 614 conjugacy classes of subgroups — too many to draw. Only its 140 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. C8×C22⋊#6157 | C2 | semidirect |
| 4. #20289557 | C2 | semidirect |
| 12. #16811469 | C4 | semidirect |
| 13. #16811466 | C4 | semidirect |
| 18. C2×#13133146 | C4 | semidirect |
| 19. C2×C22⋊#88322 | C4 | semidirect |
| 21. C2×C8×Dic53 | C4 | semidirect |
| 22. C23×C8×C53 | C4 | semidirect |
| 26. #13133275 | C8 | direct (N × H) |
| 75. C22⋊#6157 | C2×C8 | semidirect |
| 103. C23×C53 | C4×C8 | semidirect |
| 128. C2×Dic53 | C4×C8 | semidirect |
| 136. C8×C53 | #99 | semidirect |
| 176. C23×C8 | #6157 | semidirect |
| 192. C53 | C8×#99 | semidirect |
| 278. C23 | C8×#6157 | semidirect |
| 308. C8 | #13133275 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133275 | 2 |
| C8×C22⋊#6157 | 2 |
| #20289950 | 2 |
| #20289557 | 2 |
| C2×C8×C22⋊D53 | 2 |
| C8×#99 | 53 |