Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
774 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20277556 | C2 | semidirect |
| 2. #20275552 | C2 | semidirect |
| 3. #20274659 | C2 | semidirect |
| 4. #20273231 | C2 | semidirect |
| 5. #20272620 | C2 | semidirect |
| 6. #20272600 | C2 | semidirect |
| 22. C2×AGL(1,ℤ/8)×C53 | C4 | semidirect |
| 27. C53×#417 | C4 | semidirect |
| 155. Q8×C53 | #99 | semidirect |
| 246. C2×AGL(1,ℤ/8) | Dic53 | semidirect |
| 253. #417 | Dic53 | semidirect |
| 266. C53 | #9368 | semidirect |
| 393. Q8 | #13133132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277556 | 2 |
| #20275552 | 2 |
| #20274659 | 2 |
| #20273231 | 2 |
| #20272620 | 2 |
| #20272600 | 2 |
| C53×#3006 | 2 |
| #9368 | 53 |