Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 114 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. #20290428 | C2 | semidirect |
| 4. #20289927 | C2 | semidirect |
| 5. #20289547 | C2 | semidirect |
| 6. #20289542 | C2 | semidirect |
| 8. #16811674 | C4 | semidirect |
| 9. #16811657 | C4 | semidirect |
| 25. Q8⋊#88322 | C4 | semidirect |
| 26. #16810352 | C4 | semidirect |
| 27. #16810350 | C4 | semidirect |
| 28. C53×Q8⋊C8 | C4 | semidirect |
| 86. C4×#6157 | M16 | semidirect |
| 194. Q8⋊C8 | #6157 | semidirect |
| 199. C53 | #8195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291523 | 2 |
| C4×#13133282 | 2 |
| #20290428 | 2 |
| #20289927 | 2 |
| #20289547 | 2 |
| #20289542 | 2 |
| #20273096 | 2 |
| #8195 | 53 |