Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
290 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 130 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. #88324⋊C16 | C2 | semidirect |
| 4. #20289626 | C2 | semidirect |
| 59. C16×C53 | M16 | semidirect |
| 61. #11719908 | M16 | semidirect |
| 115. C53 | #11408 | semidirect |
| 157. C16 | #11719936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291075 | 2 |
| C8×#11719936 | 2 |
| #88324⋊C16 | 2 |
| #20289626 | 2 |
| C4×C16×D53 | 2 |
| #11408 | 53 |