Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1034 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1034 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20277293 | C2 | semidirect |
| 2. #20274636 | C2 | semidirect |
| 3. #20273244 | C2 | semidirect |
| 4. #20272568 | C2 | semidirect |
| 14. C2×#127×C53 | C4 | semidirect |
| 19. C53×#390 | C4 | semidirect |
| 32. #13133124 | D4 | semidirect |
| 42. C22×D4×C53 | C2×C4 | semidirect |
| 50. C2×C4⋊C4×C53 | C2×C4 | semidirect |
| 55. C2×C42×C53 | C2×C4 | semidirect |
| 227. C2×#127 | Dic53 | semidirect |
| 235. #390 | Dic53 | semidirect |
| 241. C53 | #9463 | semidirect |
| 251. C22×D4 | C2×Dic53 | semidirect |
| 261. C2×C4⋊C4 | C2×Dic53 | semidirect |
| 271. C2×C42 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277293 | 2 |
| #20274636 | 2 |
| #20273244 | 2 |
| #20272568 | 2 |
| C53×#2433 | 2 |
| #9463 | 53 |