Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
558 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20273110 | C2 | semidirect |
| 4. #20272548 | C2 | semidirect |
| 56. C2×Q8×C53 | M16 | semidirect |
| 84. C42×C53 | M16 | semidirect |
| 173. C53 | #8961 | semidirect |
| 209. C2×Q8 | #11719917 | semidirect |
| 240. C42 | #11719917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283756 | 2 |
| #20273110 | 2 |
| #20273036 | 2 |
| #20272548 | 2 |
| C4×#124×C53 | 2 |
| #8961 | 53 |