Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
624 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20283279 | C2 | semidirect |
| 3. #20273382 | C2 | semidirect |
| 4. #20272574 | C2 | semidirect |
| 5. C53×#1458 | C2 | semidirect |
| 42. C4⋊#88322 | D4 | semidirect |
| 181. #1458 | D53 | semidirect |
| 207. C53 | #9197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283279 | 2 |
| #20280465 | 2 |
| #20273382 | 2 |
| #20272574 | 2 |
| C53×#1458 | 2 |
| #9197 | 53 |