Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
756 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 215 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. #20275204 | C2 | semidirect |
| 2. #20275197 | C2 | semidirect |
| 3. #20275114 | C2 | semidirect |
| 4. #20275099 | C2 | semidirect |
| 5. #20274864 | C2 | semidirect |
| 20. C53×#496 | C4 | semidirect |
| 21. C53×#493 | C4 | semidirect |
| 22. C53×#492 | C4 | semidirect |
| 39. C2×SD16×C53 | C2×C4 | semidirect |
| 40. C2×D8×C53 | C2×C4 | semidirect |
| 42. C4⋊Q8×C53 | C2×C4 | semidirect |
| 46. #127×C53 | C2×C4 | semidirect |
| 47. #124×C53 | C2×C4 | semidirect |
| 51. #97×C53 | C2×C4 | semidirect |
| 52. C4×C8×C53 | C2×C4 | semidirect |
| 148. #496 | Dic53 | semidirect |
| 149. #493 | Dic53 | semidirect |
| 150. #492 | Dic53 | semidirect |
| 160. C53 | #23361 | semidirect |
| 166. C2×SD16 | C2×Dic53 | semidirect |
| 167. C2×D8 | C2×Dic53 | semidirect |
| 172. C4⋊Q8 | C2×Dic53 | semidirect |
| 176. #127 | C2×Dic53 | semidirect |
| 177. #124 | C2×Dic53 | semidirect |
| 188. #97 | C2×Dic53 | semidirect |
| 189. C4×C8 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275204 | 2 |
| #20275197 | 2 |
| #20275114 | 2 |
| #20275099 | 2 |
| #20274864 | 2 |
| C53×#3151 | 2 |
| #23361 | 53 |