Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
436 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 70. C2×Q8×C53 | Q16 | semidirect |
| 100. C4⋊Dic53 | Q16 | semidirect |
| 211. C53 | #7784 | semidirect |
| 259. C2×Q8 | #11719925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282679 | 2 |
| #20276040 | 2 |
| #20275815 | 2 |
| #20272541 | 2 |
| #20272540 | 2 |
| #20272537 | 2 |
| C53×#2024 | 2 |
| #7784 | 53 |