Finite Group DatabasebetaFinite Group DatabasebetaOrder 13504.
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#16809952 | C2 | semidirect |
| 4. #20269975 | C2 | semidirect |
| 6. #20269887 | C2 | semidirect |
| 7. C2×Q16×C211 | C2 | semidirect |
| 49. C211 | #497 | semidirect |
| 52. C2×Q16 | D211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16809952 | 2 |
| C2×#16809951 | 2 |
| C2×#16809949 | 2 |
| #20269975 | 2 |
| #20269966 | 2 |
| #20269887 | 2 |
| C2×Q16×C211 | 2 |
| #497 | 211 |