Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
362 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20272685 | C2 | semidirect |
| 57. Q16×C53 | M16 | semidirect |
| 137. C53 | #11664 | semidirect |
| 175. Q16 | #11719917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276518 | 2 |
| #20273471 | 2 |
| #20272685 | 2 |
| C2×C4×Q16×C53 | 2 |
| #11664 | 53 |