Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
376 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 80 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. C4⋊C8×#6157 | C2 | semidirect |
| 3. #20290285 | C2 | semidirect |
| 5. #20289607 | C2 | semidirect |
| 6. #20289542 | C2 | semidirect |
| 23. #16810370 | C4 | semidirect |
| 24. #16810368 | C4 | semidirect |
| 25. #16810367 | C4 | semidirect |
| 26. C53×#331 | C4 | semidirect |
| 196. #331 | #6157 | semidirect |
| 199. C53 | #9577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290849 | 2 |
| C4⋊C8×#6157 | 2 |
| #20290285 | 2 |
| #20290021 | 2 |
| #20289607 | 2 |
| #20289542 | 2 |
| #20273361 | 2 |
| #9577 | 53 |