Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
582 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 244 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 |
|---|---|---|
| 11. #88324⋊C8 | C4 | semidirect |
| 12. C8×#88324 | C4 | semidirect |
| 15. #16810345 | C4 | semidirect |
| 16. #16810344 | C4 | semidirect |
| 17. C53×#322 | C4 | semidirect |
| 64. #88324 | #97 | semidirect |
| 66. C8×C53 | #97 | semidirect |
| 68. #88322 | #97 | semidirect |
| 96. #322 | #6157 | semidirect |
| 98. C53 | #7846 | semidirect |
| 149. C8 | #13133271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133271 | 2 |
| #20289911 | 2 |
| C8×D53⋊C8 | 2 |
| #322×D53 | 2 |
| #7846 | 53 |