Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 454 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 |
|---|---|---|
| 1. #20283091 | C2 | semidirect |
| 4. #20272574 | C2 | semidirect |
| 5. #20272573 | C2 | semidirect |
| 6. #20272547 | C2 | semidirect |
| 44. C4⋊Q8×C53 | Q8 | semidirect |
| 45. #127×C53 | Q8 | semidirect |
| 193. C53 | #10362 | semidirect |
| 199. C4⋊Q8 | Dic106 | semidirect |
| 200. #127 | Dic106 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283091 | 2 |
| #20275544 | 2 |
| #20273275 | 2 |
| #20272574 | 2 |
| #20272573 | 2 |
| #20272547 | 2 |
| C53×#1517 | 2 |
| #10362 | 53 |