Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2130 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2130 conjugacy classes of subgroups — too many to draw. Only its 667 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. #20283097 | C2 | semidirect |
| 2. #20283082 | C2 | semidirect |
| 3. #20283030 | C2 | semidirect |
| 4. C4×#13133211 | C2 | semidirect |
| 6. #20277198 | C2 | semidirect |
| 7. C2×C43×C53 | C2 | semidirect |
| 65. C42×C53 | #41 | semidirect |
| 79. C2×C4×C53 | #126 | semidirect |
| 108. C2×C43 | D53 | semidirect |
| 130. C53 | #36641 | semidirect |
| 176. C42 | #11719945 | semidirect |
| 192. C2×C4 | #13133211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283097 | 2 |
| #20283082 | 2 |
| #20283030 | 2 |
| C4×#13133211 | 2 |
| #20277205 | 2 |
| #20277198 | 2 |
| C2×C43×C53 | 2 |
| #36641 | 53 |