Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
214 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 1. C22×#13133123 | C2 | semidirect |
| 2. C4⋊#13133123 | C2 | semidirect |
| 3. C22⋊#13133123 | C2 | semidirect |
| 4. C4×#13133123 | C2 | semidirect |
| 17. #13133123 | D4 | direct (N × H) |
| 43. D4×C53 | C32 | semidirect |
| 57. C22×C53 | C2×C32 | semidirect |
| 61. C4×C53 | C2×C32 | semidirect |
| 82. C53 | D4×C32 | semidirect |
| 111. D4 | #13133123 | direct (N × H) |
| 124. C22 | C2×#13133123 | semidirect |
| 128. C4 | C2×#13133123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133123 | 2 |
| C4⋊#13133123 | 2 |
| C22⋊#13133123 | 2 |
| C4×#13133123 | 2 |
| D4×C16×C53 | 2 |
| D4×C32 | 53 |