Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
762 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 762 conjugacy classes of subgroups — too many to draw. Only its 135 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. #20277329 | C2 | semidirect |
| 2. #20273283 | C2 | semidirect |
| 3. C2×#16810347 | C2 | semidirect |
| 4. #20272582 | C2 | semidirect |
| 16. C53×#397 | C4 | semidirect |
| 18. C53×#392 | C4 | semidirect |
| 32. #13133124 | D4 | semidirect |
| 36. C22×D4×C53 | C2×C4 | semidirect |
| 44. C2×C4⋊C4×C53 | C2×C4 | semidirect |
| 54. #95×C53 | C2×C4 | semidirect |
| 225. #397 | Dic53 | semidirect |
| 227. #392 | Dic53 | semidirect |
| 235. C53 | #9203 | semidirect |
| 239. C22×D4 | C2×Dic53 | semidirect |
| 251. C2×C4⋊C4 | C2×Dic53 | semidirect |
| 269. #95 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277329 | 2 |
| #20273283 | 2 |
| C2×#16810347 | 2 |
| #20272582 | 2 |
| C53×#2617 | 2 |
| #9203 | 53 |