Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
912 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20285658 | C2 | semidirect |
| 2. #20285656 | C2 | semidirect |
| 4. #20275691 | C2 | semidirect |
| 5. #20273384 | C2 | semidirect |
| 6. #20272547 | C2 | semidirect |
| 7. C53×#1545 | C2 | semidirect |
| 35. #13133217 | D4 | semidirect |
| 36. #13133217 | D4 | semidirect |
| 54. C4⋊#88322 | D4 | semidirect |
| 70. C4⋊C8×C53 | D4 | semidirect |
| 123. C4×Dic53 | SD16 | semidirect |
| 198. #1545 | D53 | semidirect |
| 227. C53 | #10290 | semidirect |
| 265. C4⋊C8 | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285658 | 2 |
| #20285656 | 2 |
| #20283109 | 2 |
| #20275691 | 2 |
| #20273384 | 2 |
| #20272547 | 2 |
| C53×#1545 | 2 |
| #10290 | 53 |