Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
380 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20272822 | C2 | semidirect |
| 5. #20272817 | C2 | semidirect |
| 6. #20272816 | C2 | semidirect |
| 7. C53×#1386 | C2 | semidirect |
| 15. #16810658 | C4 | semidirect |
| 16. #106×D53 | C4 | semidirect |
| 150. #1386 | D53 | semidirect |
| 173. C53 | #12873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283306 | 2 |
| #20276335 | 2 |
| #20274758 | 2 |
| #20272822 | 2 |
| #20272817 | 2 |
| #20272816 | 2 |
| C53×#1386 | 2 |
| #12873 | 53 |