Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 3. C8×Dic212 | C2 | semidirect |
| 4. #20272787 | C2 | semidirect |
| 5. #20272680 | C2 | semidirect |
| 7. C53×#1312 | C2 | semidirect |
| 61. Dic212 | M16 | semidirect |
| 108. #1312 | D53 | semidirect |
| 128. C53 | #12075 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133162 | 2 |
| #20273601 | 2 |
| C8×Dic212 | 2 |
| #20272787 | 2 |
| #20272680 | 2 |
| #20272677 | 2 |
| C53×#1312 | 2 |
| #12075 | 53 |