Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 95 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. #20276470 | C2 | semidirect |
| 4. #20276320 | C2 | semidirect |
| 6. #20272796 | C2 | semidirect |
| 7. C53×#1378 | C2 | semidirect |
| 143. #1378 | D53 | semidirect |
| 165. C53 | #13129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276470 | 2 |
| #20276344 | 2 |
| #20276335 | 2 |
| #20276320 | 2 |
| #20274554 | 2 |
| #20272796 | 2 |
| C53×#1378 | 2 |
| #13129 | 53 |