Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
332 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 3. C2×C4×#11719908 | C2 | semidirect |
| 5. #20272810 | C2 | semidirect |
| 6. #20272808 | C2 | semidirect |
| 7. C53×#1945 | C2 | semidirect |
| 15. #16810426 | C4 | semidirect |
| 16. #16810423 | C4 | semidirect |
| 137. #1945 | D53 | semidirect |
| 160. C53 | #13151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810429 | 2 |
| #20276420 | 2 |
| C2×C4×#11719908 | 2 |
| #20275603 | 2 |
| #20272810 | 2 |
| #20272808 | 2 |
| C53×#1945 | 2 |
| #13151 | 53 |