Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
436 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 68. C2×Q8×C53 | Q16 | semidirect |
| 95. C4⋊C4×C53 | Q16 | semidirect |
| 211. C53 | #7784 | semidirect |
| 259. C2×Q8 | #11719925 | semidirect |
| 294. C4⋊C4 | #11719925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276043 | 2 |
| #20275856 | 2 |
| #20275814 | 2 |
| #20272541 | 2 |
| #20272538 | 2 |
| C53×#2806 | 2 |
| #7784 | 53 |