Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
802 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 235 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×#16810974 | C2 | semidirect |
| 3. #20274327 | C2 | direct (N × H) |
| 4. C2×C82×C53 | C2 | semidirect |
| 8. #16810974 | C22 | semidirect |
| 14. C82×C53 | C22 | semidirect |
| 72. C2×C82 | D53 | semidirect |
| 73. C2×C53 | #1711 | semidirect |
| 85. C82 | C2×D53 | semidirect |
| 86. C53 | C2×#1711 | semidirect |
| 141. C2 | #20274327 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810974 | 2 |
| C2×#16810970 | 2 |
| #20274327 | 2 |
| C2×C82×C53 | 2 |
| C2×#1711 | 53 |