Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
550 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 110 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. #20289535 | C2 | semidirect |
| 4. #20289533 | C2 | semidirect |
| 61. C2×Q8×C53 | M16 | semidirect |
| 93. C4⋊C4×C53 | M16 | semidirect |
| 216. C53 | #7617 | semidirect |
| 255. C2×Q8 | #11719940 | semidirect |
| 292. C4⋊C4 | #11719940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290571 | 2 |
| #20290378 | 2 |
| #20289535 | 2 |
| #20289533 | 2 |
| C22⋊Q8×Dic53 | 2 |
| #7617 | 53 |