Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
406 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20285238 | C2 | semidirect |
| 5. #20272822 | C2 | semidirect |
| 6. #20272798 | C2 | semidirect |
| 7. C53×#1386 | C2 | semidirect |
| 29. C2×D424 | Q8 | semidirect |
| 149. #1386 | D53 | semidirect |
| 171. C53 | #13367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285238 | 2 |
| #20276432 | 2 |
| #20276430 | 2 |
| #20275589 | 2 |
| #20272822 | 2 |
| #20272798 | 2 |
| C53×#1386 | 2 |
| #13367 | 53 |