Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
394 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 147 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. #20272657 | C2 | direct (N × H) |
| 105. C2×C53 | #1323 | semidirect |
| 118. C53 | C2×#1323 | semidirect |
| 206. C2 | #20272657 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊#11719908 | 2 |
| #20272657 | 2 |
| C2×C53×#424 | 2 |
| C2×#1323 | 53 |