Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
626 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 168 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. #20289555 | C2 | semidirect |
| 62. C2×C8×C53 | M16 | semidirect |
| 75. C2×#88322 | M16 | semidirect |
| 140. C53 | #7919 | semidirect |
| 189. C2×C8 | #11719936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291392 | 2 |
| #20289555 | 2 |
| C2×#97×D53 | 2 |
| #7919 | 53 |