Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
500 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 118 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. #20290642 | C2 | semidirect |
| 2. #20290429 | C2 | semidirect |
| 3. #20289533 | C2 | semidirect |
| 48. C4×D4×C53 | C8 | semidirect |
| 196. C53 | #7580 | semidirect |
| 202. C4×D4 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290642 | 2 |
| #20290429 | 2 |
| #20289533 | 2 |
| #20289531 | 2 |
| #20277180 | 2 |
| #7580 | 53 |