Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
998 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 112 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. #20290579 | C2 | semidirect |
| 2. #20290228 | C2 | semidirect |
| 3. #20290040 | C2 | semidirect |
| 4. #20289954 | C2 | semidirect |
| 164. D4×C53 | #100 | semidirect |
| 265. C53 | #8393 | semidirect |
| 408. D4 | #13133277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290579 | 2 |
| #20290228 | 2 |
| #20290040 | 2 |
| #20289954 | 2 |
| C2×#16811272 | 2 |
| #8393 | 53 |