Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
254 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 74 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. #20290296 | C2 | semidirect |
| 2. D8×#88324 | C2 | semidirect |
| 3. #20289749 | C2 | semidirect |
| 4. #20289670 | C2 | semidirect |
| 5. #20289669 | C2 | semidirect |
| 6. #20289626 | C2 | semidirect |
| 35. #13133158 | C8 | semidirect |
| 56. D8×C53 | C2×C8 | semidirect |
| 65. D424 | C2×C8 | semidirect |
| 68. #11719908 | C2×C8 | semidirect |
| 134. C53 | #12045 | semidirect |
| 163. D8 | D53⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290296 | 2 |
| D8×#88324 | 2 |
| #20289749 | 2 |
| #20289670 | 2 |
| #20289669 | 2 |
| #20289626 | 2 |
| #20276559 | 2 |
| #12045 | 53 |