Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
230 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 2. #20289873 | C2 | direct (N × H) |
| 44. C2×Dic53 | C32 | semidirect |
| 60. Dic53 | C2×C32 | semidirect |
| 64. C2×C53 | C4⋊C32 | semidirect |
| 75. C53 | C2×C4⋊C32 | semidirect |
| 125. C2 | #20289873 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133267 | 2 |
| #20289873 | 2 |
| C2×C16×Dic53 | 2 |
| C2×C4⋊C32 | 53 |