Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1422 conjugacy classes of subgroups; only the 347 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 347 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 |
|---|---|---|
| 66. C4×Dic53 | Q16 | semidirect |
| 94. C4×C53 | #494 | semidirect |
| 98. Dic53 | #494 | semidirect |
| 123. C53 | #33302 | semidirect |
| 197. C4 | #16811001 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811003 | 2 |
| C2×#16811002 | 2 |
| C2×#16811001 | 2 |
| #20283111 | 2 |
| C4×C8×Dic53 | 2 |
| C2×C53×#494 | 2 |
| #33302 | 53 |