Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
222 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 85 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. Q8×#11719908 | C2 | semidirect |
| 4. #20272784 | C2 | semidirect |
| 6. #20272634 | C2 | semidirect |
| 7. C53×Q8⋊C16 | C2 | semidirect |
| 70. Q8×C53 | M32 | semidirect |
| 106. Q8⋊C16 | D53 | semidirect |
| 128. C53 | #12056 | semidirect |
| 176. Q8 | #13133156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11719908 | 2 |
| #20276546 | 2 |
| C8×#11719924 | 2 |
| #20272784 | 2 |
| #20272671 | 2 |
| #20272634 | 2 |
| C53×Q8⋊C16 | 2 |
| #12056 | 53 |