Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1006 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 1006 conjugacy classes of subgroups — too many to draw. Only its 320 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. #20290633 | C2 | semidirect |
| 104. D53 | #1832 | semidirect |
| 117. C53 | C2×#1832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D53⋊(C4⋊C8) | 2 |
| #20290633 | 2 |
| #20290376 | 2 |
| #376×D53 | 2 |
| C2×#1832 | 53 |