Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
542 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #20273470 | C2 | semidirect |
| 4. #20273396 | C2 | semidirect |
| 6. M16×#88322 | C2 | semidirect |
| 7. C53×#1997 | C2 | semidirect |
| 81. M16×C53 | SD16 | semidirect |
| 131. #88322 | #100 | semidirect |
| 150. #1997 | D53 | semidirect |
| 179. C53 | #9793 | semidirect |
| 238. M16 | #11719924 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810997 | 2 |
| #20275555 | 2 |
| #20273470 | 2 |
| #20273396 | 2 |
| #20273384 | 2 |
| M16×#88322 | 2 |
| C53×#1997 | 2 |
| #9793 | 53 |