Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 40. #13133136 | C8 | semidirect |
| 45. #101×C53 | C8 | semidirect |
| 97. #88324 | #101 | direct (N × H) |
| 139. C53 | C8×#101 | semidirect |
| 156. #101 | #88324 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#88324 | 2 |
| #20289958 | 2 |
| M16×#88324 | 2 |
| #20289561 | 2 |
| #101×Dic53 | 2 |
| C8×#101 | 53 |