Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #20285204 | C2 | semidirect |
| 3. #20276452 | C2 | semidirect |
| 4. #20276435 | C2 | semidirect |
| 5. #20275614 | C2 | semidirect |
| 6. #20272802 | C2 | semidirect |
| 7. C2×C53×#510 | C2 | semidirect |
| 207. C2×#510 | D53 | semidirect |
| 244. C53 | #13335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287849 | 2 |
| #20285204 | 2 |
| #20276452 | 2 |
| #20276435 | 2 |
| #20275614 | 2 |
| #20272802 | 2 |
| C2×C53×#510 | 2 |
| #13335 | 53 |