Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
998 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 108 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. C4×#13133277 | C2 | semidirect |
| 2. #20290176 | C2 | semidirect |
| 3. #20290057 | C2 | semidirect |
| 4. #20289974 | C2 | semidirect |
| 162. Q8×C53 | #100 | semidirect |
| 259. C53 | #8369 | semidirect |
| 395. Q8 | #13133277 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133277 | 2 |
| #20290176 | 2 |
| #20290057 | 2 |
| #20289974 | 2 |
| C2×#16811284 | 2 |
| #8369 | 53 |