Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
842 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 842 conjugacy classes of subgroups — too many to draw. Only its 216 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 |
|---|---|---|
| 8. C4×C4⋊#6157 | C4 | semidirect |
| 14. C2×#13133128 | C4 | semidirect |
| 15. C2×C8×Dic53 | C4 | semidirect |
| 16. C2×#97×C53 | C4 | semidirect |
| 63. C2×C8×C53 | C4⋊C4 | semidirect |
| 73. C2×#88322 | C4⋊C4 | semidirect |
| 120. Dic53 | H(3,ℤ/4) | semidirect |
| 137. C2×#97 | #6157 | semidirect |
| 144. C53 | #10837 | semidirect |
| 191. C2×C8 | C4⋊#6157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291164 | 2 |
| C2×#16811491 | 2 |
| C2×#16810575 | 2 |
| #10837 | 53 |