Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20274932 | C2 | semidirect |
| 5. #20274929 | C2 | semidirect |
| 6. #20272841 | C2 | semidirect |
| 7. C53×#1394 | C2 | semidirect |
| 21. #16810419 | C4 | semidirect |
| 57. #13133136 | C2×C4 | semidirect |
| 70. #101×C53 | C2×C4 | semidirect |
| 208. #1394 | D53 | semidirect |
| 235. C53 | #12972 | semidirect |
| 274. #101 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277826 | 2 |
| C2×#16810419 | 2 |
| #20275116 | 2 |
| #20274932 | 2 |
| #20274929 | 2 |
| #20272841 | 2 |
| C53×#1394 | 2 |
| #12972 | 53 |