Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
398 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 86 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. C2×#16811551 | C2 | semidirect |
| 4. #20290823 | C2 | semidirect |
| 5. #20289776 | C2 | semidirect |
| 6. (C2×#6157)⋊C16 | C2 | semidirect |
| 23. #16810428 | C4 | semidirect |
| 24. #16810426 | C4 | semidirect |
| 25. #16810424 | C4 | semidirect |
| 26. C53×#357 | C4 | semidirect |
| 184. #357 | #6157 | semidirect |
| 186. C53 | #12939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811665 | 2 |
| C2×#16811551 | 2 |
| C2×#16811537 | 2 |
| #20290823 | 2 |
| #20289776 | 2 |
| (C2×#6157)⋊C16 | 2 |
| #20276419 | 2 |
| #12939 | 53 |