Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 344 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 344 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. #20291138 | C2 | direct (N × H) |
| 2. C2×#16811555 | C2 | semidirect |
| 3. C22×#13133267 | C2 | semidirect |
| 5. #16811555 | C22 | semidirect |
| 8. C2×#13133267 | C22 | semidirect |
| 61. C2×C53 | #2258 | semidirect |
| 72. C53 | C2×#2258 | semidirect |
| 115. C2 | #20291138 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291138 | 2 |
| C2×#16811555 | 2 |
| C22×#13133267 | 2 |
| C2×#16811040 | 2 |
| C2×#2258 | 53 |