Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
642 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 207 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. #20275677 | C2 | semidirect |
| 3. #20274872 | C2 | semidirect |
| 4. C2×C8×#88322 | C2 | semidirect |
| 16. C53×#492 | C4 | semidirect |
| 74. C2×#88322 | SD16 | semidirect |
| 101. C8×C53 | #102 | semidirect |
| 135. #492 | Dic53 | semidirect |
| 143. C53 | #9820 | semidirect |
| 228. C8 | #13133138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275677 | 2 |
| #20275522 | 2 |
| #20274872 | 2 |
| C2×C8×#88322 | 2 |
| C2×C53×#492 | 2 |
| #9820 | 53 |