Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
430 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 89. #88322 | #101 | semidirect |
| 127. C53 | #8165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#88322 | 2 |
| C4×#13133136 | 2 |
| #20273005 | 2 |
| #20272564 | 2 |
| C53×#1461 | 2 |
| #8165 | 53 |