Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
604 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 604 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 |
|---|---|---|
| 1. #20275949 | C2 | semidirect |
| 2. #20275802 | C2 | semidirect |
| 4. #20272541 | C2 | semidirect |
| 5. #20272538 | C2 | semidirect |
| 6. #20272536 | C2 | semidirect |
| 7. C53×#2732 | C2 | semidirect |
| 72. C2×Q8×C53 | D8 | semidirect |
| 76. C2×D4×C53 | SD16 | semidirect |
| 230. #2732 | D53 | semidirect |
| 265. C53 | #7735 | semidirect |
| 311. C2×Q8 | #11719922 | semidirect |
| 333. C2×D4 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275949 | 2 |
| #20275802 | 2 |
| #20275785 | 2 |
| #20272541 | 2 |
| #20272538 | 2 |
| #20272536 | 2 |
| C53×#2732 | 2 |
| #7735 | 53 |