Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
912 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 111 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. #20285653 | C2 | semidirect |
| 3. #20273384 | C2 | semidirect |
| 4. #20272548 | C2 | semidirect |
| 5. C53×#1994 | C2 | semidirect |
| 31. C4⋊#88322 | D4 | semidirect |
| 36. C4⋊Q8×C53 | D4 | semidirect |
| 71. C42×C53 | SD16 | semidirect |
| 120. #1994 | D53 | semidirect |
| 140. C53 | #10290 | semidirect |
| 147. C4⋊Q8 | D212 | semidirect |
| 195. C42 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285653 | 2 |
| #20283110 | 2 |
| #20273384 | 2 |
| #20272548 | 2 |
| C53×#1994 | 2 |
| #10290 | 53 |