Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1342 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1342 conjugacy classes of subgroups — too many to draw. Only its 232 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. #20291304 | C2 | semidirect |
| 2. #20289992 | C2 | semidirect |
| 3. #20289972 | C2 | semidirect |
| 4. #20289952 | C2 | semidirect |
| 120. C2×C4×C53 | #131 | semidirect |
| 188. C53 | #17419 | semidirect |
| 300. C2×C4 | #13133305 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291304 | 2 |
| #20289992 | 2 |
| #20289972 | 2 |
| #20289952 | 2 |
| C2×#16811295 | 2 |
| #17419 | 53 |