Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
440 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20274830 | C2 | semidirect |
| 3. #20274567 | C2 | semidirect |
| 4. #20272541 | C2 | semidirect |
| 7. C53×#1272 | C2 | semidirect |
| 193. #1272 | D53 | semidirect |
| 223. C53 | #7696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283089 | 2 |
| #20274830 | 2 |
| #20274567 | 2 |
| #20272541 | 2 |
| #20272535 | 2 |
| C53×#1272 | 2 |
| #7696 | 53 |