Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 140 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 |
|---|---|---|
| 3. C8×#11719940 | C2 | semidirect |
| 4. #20289560 | C2 | semidirect |
| 25. #13133277 | C8 | direct (N × H) |
| 73. #11719940 | C2×C8 | semidirect |
| 129. C8×C53 | #100 | semidirect |
| 184. C53 | C8×#100 | semidirect |
| 293. C8 | #13133277 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133277 | 2 |
| #20289954 | 2 |
| C8×#11719940 | 2 |
| #20289560 | 2 |
| C2×C8×C22⋊D53 | 2 |
| C8×#100 | 53 |