Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 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. #20284431 | C2 | semidirect |
| 2. #20284359 | C2 | semidirect |
| 3. C2×#16810436 | C2 | semidirect |
| 4. #20276451 | C2 | semidirect |
| 5. #20276344 | C2 | semidirect |
| 6. #20272830 | C2 | semidirect |
| 7. C2×C53×#509 | C2 | semidirect |
| 54. #13133153 | D4 | semidirect |
| 66. C2×Q16×C53 | D4 | semidirect |
| 74. C2×D8×C53 | D4 | semidirect |
| 79. M32×C53 | D4 | semidirect |
| 205. C2×#509 | D53 | semidirect |
| 242. C53 | #13310 | semidirect |
| 255. C2×Q16 | C22⋊D53 | semidirect |
| 263. C2×D8 | C22⋊D53 | semidirect |
| 283. M32 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284431 | 2 |
| #20284359 | 2 |
| C2×#16810436 | 2 |
| #20276451 | 2 |
| #20276344 | 2 |
| #20272830 | 2 |
| C2×C53×#509 | 2 |
| #13310 | 53 |