Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
238 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20272784 | C2 | semidirect |
| 4. #20272778 | C2 | semidirect |
| 106. C53 | #12016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276518 | 2 |
| C8×#11719917 | 2 |
| #20272784 | 2 |
| #20272778 | 2 |
| C2×C53×C4⋊C16 | 2 |
| #12016 | 53 |