Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
568 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 568 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 |
|---|---|---|
| 1. #20287849 | C2 | semidirect |
| 2. #20285196 | C2 | semidirect |
| 3. #20276452 | C2 | semidirect |
| 4. #20276431 | C2 | semidirect |
| 5. #20275614 | C2 | semidirect |
| 6. #20272802 | C2 | semidirect |
| 7. C2×C53×#509 | C2 | semidirect |
| 58. C2×#11719908 | D4 | semidirect |
| 71. C2×Q16×C53 | D4 | semidirect |
| 79. C2×D8×C53 | D4 | semidirect |
| 84. M32×C53 | D4 | semidirect |
| 212. C2×#509 | D53 | semidirect |
| 250. C53 | #13334 | semidirect |
| 265. C2×Q16 | C22⋊D53 | semidirect |
| 277. C2×D8 | C22⋊D53 | semidirect |
| 295. M32 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287849 | 2 |
| #20285196 | 2 |
| #20276452 | 2 |
| #20276431 | 2 |
| #20275614 | 2 |
| #20272802 | 2 |
| C2×C53×#509 | 2 |
| #13334 | 53 |