Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
724 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 96 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. C4×D4×#6157 | C2 | semidirect |
| 2. #20290849 | C2 | semidirect |
| 3. #20290095 | C2 | semidirect |
| 4. #20290041 | C2 | semidirect |
| 5. #20289612 | C2 | semidirect |
| 6. #20289542 | C2 | semidirect |
| 25. #16810904 | C4 | semidirect |
| 26. #16810903 | C4 | semidirect |
| 27. #16810815 | C4 | semidirect |
| 32. C53×#459 | C4 | semidirect |
| 60. #13133217 | C2×C4 | semidirect |
| 76. C4⋊#88322 | C2×C4 | semidirect |
| 83. #127×C53 | C2×C4 | semidirect |
| 85. C4⋊C8×C53 | C2×C4 | semidirect |
| 135. C4×#6157 | D8 | semidirect |
| 181. D4×C53 | #104 | semidirect |
| 201. D212 | #104 | semidirect |
| 276. #459 | #6157 | semidirect |
| 293. C53 | #9233 | semidirect |
| 302. #127 | C2×#6157 | semidirect |
| 335. C4⋊C8 | C2×#6157 | semidirect |
| 439. D4 | #13133281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×#6157 | 2 |
| #20290849 | 2 |
| #20290095 | 2 |
| #20290041 | 2 |
| #20289612 | 2 |
| #20289542 | 2 |
| #20284714 | 2 |
| #9233 | 53 |