Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 89. C2×Q8×C53 | Q16 | semidirect |
| 233. C53 | #10003 | semidirect |
| 293. C2×Q8 | #11719925 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284750 | 2 |
| #20280077 | 2 |
| #20273279 | 2 |
| #20273143 | 2 |
| #20273110 | 2 |
| #20272575 | 2 |
| C53×#3078 | 2 |
| #10003 | 53 |