Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
360 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 100 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. #20291076 | C2 | semidirect |
| 2. C4×#13133291 | C2 | semidirect |
| 3. #20289682 | C2 | semidirect |
| 4. #20289666 | C2 | semidirect |
| 110. D212 | M32 | semidirect |
| 116. Dic106 | M32 | semidirect |
| 169. C53 | #11615 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291076 | 2 |
| C4×#13133291 | 2 |
| #20289682 | 2 |
| #20289666 | 2 |
| #20283671 | 2 |
| #11615 | 53 |