Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
394 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 106 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. C2×#16811551 | C2 | semidirect |
| 3. #20289775 | C2 | semidirect |
| 98. C22×C53 | #368 | semidirect |
| 105. C2×D53 | #368 | semidirect |
| 134. C53 | #12837 | semidirect |
| 222. C22 | #16811551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811551 | 2 |
| #20290595 | 2 |
| #20289775 | 2 |
| C22×C16×D53 | 2 |
| #12837 | 53 |