Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
| 91. C2×Dic106 | Q16 | semidirect |
| 216. C53 | #7759 | semidirect |
| 271. C2×Q8 | #11719925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282708 | 2 |
| #20275853 | 2 |
| #20275815 | 2 |
| #20272541 | 2 |
| #20272540 | 2 |
| C53×#2024 | 2 |
| #7759 | 53 |