Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
372 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 1. #20291073 | C2 | semidirect |
| 2. #20290272 | C2 | semidirect |
| 3. #20289671 | C2 | semidirect |
| 4. #20289669 | C2 | semidirect |
| 70. Q16×C53 | M16 | semidirect |
| 73. D8×C53 | M16 | semidirect |
| 173. C53 | #11660 | semidirect |
| 219. Q16 | #11719940 | semidirect |
| 222. D8 | #11719940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291073 | 2 |
| #20290272 | 2 |
| #20289671 | 2 |
| #20289669 | 2 |
| #135×Dic53 | 2 |
| #11660 | 53 |