Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
392 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 3. #20290285 | C2 | semidirect |
| 4. #20290270 | C2 | semidirect |
| 5. #20289612 | C2 | semidirect |
| 6. #20289550 | C2 | semidirect |
| 25. Q8⋊#88322 | C4 | semidirect |
| 26. #16810352 | C4 | semidirect |
| 27. #16810350 | C4 | semidirect |
| 28. C53×Q8⋊C8 | C4 | semidirect |
| 206. Q8⋊C8 | #6157 | semidirect |
| 209. C53 | #8905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291415 | 2 |
| #20290588 | 2 |
| #20290285 | 2 |
| #20290270 | 2 |
| #20289612 | 2 |
| #20289550 | 2 |
| #20273096 | 2 |
| #8905 | 53 |