Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
228 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20272560 | C2 | semidirect |
| 3. C53×#1375 | C2 | semidirect |
| 14. C2×Dic212 | C8 | semidirect |
| 16. C2×D424 | C8 | semidirect |
| 103. #1375 | D53 | semidirect |
| 117. C53 | #7109 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275608 | 2 |
| #20272560 | 2 |
| C53×#1375 | 2 |
| #7109 | 53 |