Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
324 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 1. #20291052 | C2 | semidirect |
| 4. C2×#16811512 | C2 | semidirect |
| 5. #20289770 | C2 | semidirect |
| 6. #20289760 | C2 | semidirect |
| 161. C53 | #13125 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291052 | 2 |
| C2×#16811522 | 2 |
| #20290947 | 2 |
| C2×#16811512 | 2 |
| #20289770 | 2 |
| #20289760 | 2 |
| #20274551 | 2 |
| #13125 | 53 |