Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
362 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 3. #20289676 | C2 | semidirect |
| 4. #20289675 | C2 | semidirect |
| 69. Q16×C53 | M16 | semidirect |
| 91. Dic212 | M16 | semidirect |
| 166. C53 | #11664 | semidirect |
| 214. Q16 | #11719936 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291079 | 2 |
| #20290270 | 2 |
| #20289676 | 2 |
| #20289675 | 2 |
| C4×Q16×D53 | 2 |
| #11664 | 53 |