Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
224 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 88 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. #20289737 | C2 | semidirect |
| 4. Q8⋊#11719910 | C2 | semidirect |
| 6. C8×#11719910 | C2 | semidirect |
| 67. #11719910 | SD16 | semidirect |
| 82. C8×C53 | M32 | semidirect |
| 128. C53 | #12051 | 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 |
| #20289737 | 2 |
| Q8⋊#11719910 | 2 |
| D4⋊#11719910 | 2 |
| C8×#11719910 | 2 |
| SD16×#88322 | 2 |
| #12051 | 53 |