Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 4. #20272541 | C2 | semidirect |
| 5. #20272538 | C2 | semidirect |
| 6. #20272538 | C2 | semidirect |
| 7. C53×#2805 | C2 | semidirect |
| 107. C4⋊C4×C53 | SD16 | semidirect |
| 202. #2805 | D53 | semidirect |
| 236. C53 | #7747 | semidirect |
| 327. C4⋊C4 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275949 | 2 |
| #20275802 | 2 |
| #20272541 | 2 |
| #20272538 | 2 |
| C53×#2805 | 2 |
| #7747 | 53 |