Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20277900 | C2 | semidirect |
| 5. C2×#16810364 | C2 | semidirect |
| 6. #20272597 | C2 | semidirect |
| 7. C53×#1295 | C2 | semidirect |
| 11. #16810988 | C4 | semidirect |
| 216. #1295 | D53 | semidirect |
| 247. C53 | #9002 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810988 | 2 |
| #20277900 | 2 |
| #20275539 | 2 |
| #20275538 | 2 |
| C2×#16810364 | 2 |
| #20272597 | 2 |
| C53×#1295 | 2 |
| #9002 | 53 |