Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
914 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 914 conjugacy classes of subgroups — too many to draw. Only its 135 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. #20276462 | C2 | semidirect |
| 3. #20276442 | C2 | semidirect |
| 4. C2×#16810405 | C2 | semidirect |
| 5. C53×#1811 | C2 | semidirect |
| 14. C2×#13133157 | C22 | semidirect |
| 20. C2×#108×C53 | C22 | semidirect |
| 21. C2×#108×C53 | C22 | semidirect |
| 191. #1811 | D53 | semidirect |
| 208. C2×#108 | C2×D53 | semidirect |
| 209. C2×#108 | C2×D53 | semidirect |
| 216. C53 | #12740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811423 | 2 |
| #20276462 | 2 |
| #20276442 | 2 |
| C2×#16810405 | 2 |
| C53×#1811 | 2 |
| #12740 | 53 |