Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
280 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20276990 | C2 | semidirect |
| 3. #20276943 | C2 | semidirect |
| 5. #20274312 | C2 | semidirect |
| 7. C53×#1311 | C2 | semidirect |
| 68. C16×C53 | SD16 | semidirect |
| 106. #1311 | D53 | semidirect |
| 126. C53 | #12508 | semidirect |
| 172. C16 | #11719913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276990 | 2 |
| #20276971 | 2 |
| #20276943 | 2 |
| #20276939 | 2 |
| #20274312 | 2 |
| #20274307 | 2 |
| C53×#1311 | 2 |
| #12508 | 53 |