Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
562 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 167 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. #20287690 | C2 | semidirect |
| 2. #20276940 | C2 | semidirect |
| 3. #20276849 | C2 | semidirect |
| 4. #20276750 | C2 | semidirect |
| 5. Q8×#11719908 | C2 | semidirect |
| 6. C4×#13133158 | C2 | semidirect |
| 7. Q8×D8×C53 | C2 | semidirect |
| 57. D8×C53 | #41 | semidirect |
| 75. Q8×C53 | D16 | semidirect |
| 107. Q8×D8 | D53 | semidirect |
| 134. C53 | #33925 | semidirect |
| 171. D8 | #11719949 | semidirect |
| 186. Q8 | #13133158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287690 | 2 |
| #20276940 | 2 |
| #20276849 | 2 |
| #20276750 | 2 |
| Q8×#11719908 | 2 |
| C4×#13133158 | 2 |
| Q8×D8×C53 | 2 |
| #33925 | 53 |