Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
268 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20276944 | C2 | semidirect |
| 4. #20272632 | C2 | semidirect |
| 5. C53×#1713 | C2 | semidirect |
| 75. #1713 | D53 | semidirect |
| 93. C53 | #12512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276944 | 2 |
| #20276940 | 2 |
| #20274321 | 2 |
| #20272632 | 2 |
| C53×#1713 | 2 |
| #12512 | 53 |