Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
224 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 86 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. #20289749 | C2 | semidirect |
| 4. #20289748 | C2 | semidirect |
| 5. #20289747 | C2 | semidirect |
| 6. #20289746 | C2 | semidirect |
| 64. C16×C53 | M16 | semidirect |
| 66. #11719908 | M16 | semidirect |
| 127. C53 | #12025 | semidirect |
| 171. C16 | #11719940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290277 | 2 |
| #20290272 | 2 |
| #20289749 | 2 |
| #20289748 | 2 |
| #20289747 | 2 |
| #20289746 | 2 |
| M32×Dic53 | 2 |
| #12025 | 53 |