Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 24. #13133217 | Q8 | semidirect |
| 25. #13133217 | Q8 | semidirect |
| 176. C53 | #10363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283091 | 2 |
| #20275691 | 2 |
| #20273280 | 2 |
| #20273278 | 2 |
| #20272575 | 2 |
| #20272547 | 2 |
| C53×#1286 | 2 |
| #10363 | 53 |