Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20273309 | C2 | semidirect |
| 4. #20273137 | C2 | semidirect |
| 6. C8×#11719917 | C2 | semidirect |
| 7. C4×#108×C53 | C2 | semidirect |
| 172. C4×#108 | D53 | semidirect |
| 206. C53 | #9723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285274 | 2 |
| #20273309 | 2 |
| #20273306 | 2 |
| #20273137 | 2 |
| #20273133 | 2 |
| C8×#11719917 | 2 |
| C4×#108×C53 | 2 |
| #9723 | 53 |