Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
218 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 86 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. #20291130 | C2 | semidirect |
| 3. #20289744 | C2 | semidirect |
| 4. Q8⋊#11719910 | C2 | semidirect |
| 6. #20289628 | C2 | semidirect |
| 82. C8×C53 | M32 | semidirect |
| 128. C53 | #12058 | semidirect |
| 194. C8 | #13133291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291130 | 2 |
| #20291099 | 2 |
| #20289744 | 2 |
| Q8⋊#11719910 | 2 |
| D4⋊#11719910 | 2 |
| #20289628 | 2 |
| SD16×#88322 | 2 |
| #12058 | 53 |