Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
218 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20276997 | C2 | semidirect |
| 4. #20272789 | C2 | semidirect |
| 5. #20272772 | C2 | semidirect |
| 6. #20272769 | C2 | semidirect |
| 65. C16×C53 | SD16 | semidirect |
| 125. C53 | #12453 | semidirect |
| 168. C16 | #11719923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276997 | 2 |
| #20274114 | 2 |
| #20274104 | 2 |
| #20272789 | 2 |
| #20272772 | 2 |
| #20272769 | 2 |
| D4×C16×C53 | 2 |
| #12453 | 53 |