Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
374 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 33. #13133152 | C8 | semidirect |
| 81. #88324 | #108 | semidirect |
| 123. C53 | C8×#108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290264 | 2 |
| M16×#88324 | 2 |
| C2×C8×#88324 | 2 |
| #20289548 | 2 |
| #20274616 | 2 |
| C8×#108 | 53 |