Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
286 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20276762 | C2 | semidirect |
| 4. #20272767 | C2 | semidirect |
| 5. #20272686 | C2 | semidirect |
| 7. C53×#2245 | C2 | semidirect |
| 137. #2245 | D53 | semidirect |
| 166. C53 | #12351 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20287288 | 2 |
| #20276762 | 2 |
| #20274201 | 2 |
| #20272767 | 2 |
| #20272686 | 2 |
| #20272674 | 2 |
| C53×#2245 | 2 |
| #12351 | 53 |