Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
824 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 824 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#16810392 | C2 | semidirect |
| 3. #20272719 | C2 | direct (N × H) |
| 4. C2×C53×#324 | C2 | semidirect |
| 15. #16810392 | C22 | semidirect |
| 19. C53×#324 | C22 | semidirect |
| 196. C2×#324 | D53 | semidirect |
| 201. C2×C53 | #1345 | semidirect |
| 220. #324 | C2×D53 | semidirect |
| 221. C53 | C2×#1345 | semidirect |
| 399. C2 | #20272719 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810540 | 2 |
| C2×#16810392 | 2 |
| #20272719 | 2 |
| C2×C53×#324 | 2 |
| C2×#1345 | 53 |