Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
250 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 104 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. #20289634 | C2 | semidirect |
| 4. #20289632 | C2 | semidirect |
| 59. C16×C53 | M16 | semidirect |
| 61. #11719908 | M16 | semidirect |
| 115. C53 | #11413 | semidirect |
| 157. C16 | #11719940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291077 | 2 |
| #20289924 | 2 |
| #20289634 | 2 |
| #20289632 | 2 |
| C2×#16810398 | 2 |
| #11413 | 53 |