Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1628 conjugacy classes of subgroups; only the 760 normal subgroups are shown.
This group has 1628 conjugacy classes of subgroups — too many to draw. Only its 760 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. #20291673 | C2 | semidirect |
| 2. #20291628 | C2 | semidirect |
| 3. #20291532 | C2 | semidirect |
| 4. #20291505 | C2 | semidirect |
| 114. C53 | #60332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291673 | 2 |
| #20291628 | 2 |
| #20291532 | 2 |
| #20291505 | 2 |
| #20288863 | 2 |
| #60332 | 53 |