Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
394 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 8. #16811674 | C4 | semidirect |
| 11. Q8×#88324 | C4 | semidirect |
| 26. #16810372 | C4 | semidirect |
| 27. #16810370 | C4 | semidirect |
| 28. #16810368 | C4 | semidirect |
| 29. C53×#333 | C4 | semidirect |
| 185. #333 | #6157 | semidirect |
| 191. C53 | #8254 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291504 | 2 |
| #20290512 | 2 |
| #20290099 | 2 |
| #20289931 | 2 |
| #20289612 | 2 |
| #20289607 | 2 |
| #20273369 | 2 |
| #8254 | 53 |