Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
484 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 82 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. #20290653 | C2 | semidirect |
| 4. #20290638 | C2 | semidirect |
| 5. #20289592 | C2 | semidirect |
| 6. #20289592 | C2 | semidirect |
| 27. #16810363 | C4 | semidirect |
| 28. #16810362 | C4 | semidirect |
| 29. #16810362 | C4 | semidirect |
| 30. C53×#329 | C4 | semidirect |
| 69. #13133128 | C2×C4 | semidirect |
| 70. #13133128 | C2×C4 | semidirect |
| 74. #97×C53 | C2×C4 | semidirect |
| 75. #97×C53 | C2×C4 | semidirect |
| 257. #329 | #6157 | semidirect |
| 258. C53 | #8911 | semidirect |
| 296. #97 | C2×#6157 | semidirect |
| 297. #97 | C2×#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291258 | 2 |
| #20290845 | 2 |
| #20290653 | 2 |
| #20290638 | 2 |
| #20289592 | 2 |
| #329×D53 | 2 |
| #8911 | 53 |