Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
236 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 69 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 |
|---|---|---|
| 1. #20276968 | C2 | semidirect |
| 4. #20272763 | C2 | semidirect |
| 5. C53×#1371 | C2 | semidirect |
| 61. D212 | Q32 | semidirect |
| 86. #1371 | D53 | semidirect |
| 103. C53 | #12431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276968 | 2 |
| C16×D212 | 2 |
| #20274081 | 2 |
| #20272763 | 2 |
| C53×#1371 | 2 |
| #12431 | 53 |