Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
374 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 41. #13133128 | Q8 | semidirect |
| 42. #13133128 | Q8 | semidirect |
| 59. #97×C53 | Q8 | semidirect |
| 193. C53 | #10584 | semidirect |
| 218. #97 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20282987 | 2 |
| #20274881 | 2 |
| #20274850 | 2 |
| #20272597 | 2 |
| #20272596 | 2 |
| C53×#1836 | 2 |
| #10584 | 53 |