Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
306 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 207 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 |
|---|---|---|
| 11. C2×#11719908 | C8 | semidirect |
| 24. C2×C8×C53 | C16 | semidirect |
| 68. C53 | #7136 | semidirect |
| 84. C2×C8 | #11719908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11719908 | 2 |
| C2×C82×C53 | 2 |
| #7136 | 53 |