Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
680 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #20277887 | C2 | semidirect |
| 3. C2×#16810419 | C2 | semidirect |
| 4. #20274674 | C2 | semidirect |
| 5. #20272842 | C2 | semidirect |
| 6. #20272841 | C2 | semidirect |
| 7. C53×#1793 | C2 | semidirect |
| 11. #16810796 | C4 | semidirect |
| 59. #13133136 | C2×C4 | semidirect |
| 68. 2−1+4×C53 | C2×C4 | semidirect |
| 262. #1793 | D53 | semidirect |
| 294. C53 | #13055 | semidirect |
| 299. 2−1+4 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810796 | 2 |
| #20277887 | 2 |
| C2×#16810419 | 2 |
| #20274674 | 2 |
| #20272842 | 2 |
| #20272841 | 2 |
| C53×#1793 | 2 |
| #13055 | 53 |