Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
284 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20276944 | C2 | semidirect |
| 4. #20274313 | C2 | semidirect |
| 6. C16×#88322 | C2 | semidirect |
| 7. C53×#2254 | C2 | semidirect |
| 67. C16×C53 | SD16 | semidirect |
| 87. #88322 | SD32 | semidirect |
| 100. #2254 | D53 | semidirect |
| 126. C53 | #12505 | semidirect |
| 172. C16 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276971 | 2 |
| #20276944 | 2 |
| #20276940 | 2 |
| #20274313 | 2 |
| #20274308 | 2 |
| C16×#88322 | 2 |
| C53×#2254 | 2 |
| #12505 | 53 |