Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 10. #16811003 | C4 | semidirect |
| 11. #16810974 | C4 | semidirect |
| 82. C42×C53 | Q16 | semidirect |
| 192. C53 | #9297 | semidirect |
| 268. C42 | Dic212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285665 | 2 |
| #20277463 | 2 |
| #20275696 | 2 |
| #20273395 | 2 |
| #20273280 | 2 |
| #20272574 | 2 |
| C53×#1274 | 2 |
| #9297 | 53 |