Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
528 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 528 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 |
|---|---|---|
| 2. #20276940 | C2 | semidirect |
| 3. #20276859 | C2 | semidirect |
| 4. #20276755 | C2 | semidirect |
| 5. Q8×#11719908 | C2 | semidirect |
| 6. C4×#13133160 | C2 | semidirect |
| 7. Q8×Q16×C53 | C2 | semidirect |
| 55. Q16×C53 | #41 | semidirect |
| 75. Q8×C53 | SD32 | semidirect |
| 103. Q8×Q16 | D53 | semidirect |
| 129. C53 | #33929 | semidirect |
| 161. Q16 | #11719949 | semidirect |
| 181. Q8 | #13133160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287690 | 2 |
| #20276940 | 2 |
| #20276859 | 2 |
| #20276755 | 2 |
| Q8×#11719908 | 2 |
| C4×#13133160 | 2 |
| Q8×Q16×C53 | 2 |
| #33929 | 53 |