Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 82 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. C2×#16811542 | C2 | semidirect |
| 4. #20290877 | C2 | semidirect |
| 5. #20289793 | C2 | semidirect |
| 6. #20289767 | C2 | semidirect |
| 24. #16811066 | C4 | semidirect |
| 26. #16811064 | C4 | semidirect |
| 27. #16811063 | C4 | semidirect |
| 32. C53×#510 | C4 | semidirect |
| 225. #510 | #6157 | semidirect |
| 242. C53 | #13031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291494 | 2 |
| #20291042 | 2 |
| C2×#16811542 | 2 |
| #20290877 | 2 |
| #20289793 | 2 |
| #20289767 | 2 |
| #510×D53 | 2 |
| #13031 | 53 |