Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
262 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 84. #88322 | Q32 | semidirect |
| 120. C53 | #12504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276988 | 2 |
| #20276967 | 2 |
| #20276943 | 2 |
| #20274313 | 2 |
| #20274309 | 2 |
| C16×#88322 | 2 |
| C53×#2241 | 2 |
| #12504 | 53 |