Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
538 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 127 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. #20272544 | C2 | semidirect |
| 56. C2×Q8×C53 | M16 | semidirect |
| 83. C42×C53 | M16 | semidirect |
| 172. C53 | #9103 | semidirect |
| 208. C2×Q8 | #11719917 | semidirect |
| 238. 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 |
| #20272544 | 2 |
| C53×#2326 | 2 |
| #9103 | 53 |