Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
732 conjugacy classes of subgroups; only the 243 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 243 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. #20275270 | C2 | semidirect |
| 4. #20274586 | C2 | semidirect |
| 6. C42×#88322 | C2 | semidirect |
| 7. C53×#1839 | C2 | semidirect |
| 65. C42×C53 | M16 | semidirect |
| 101. #88322 | #126 | semidirect |
| 119. #1839 | D53 | semidirect |
| 144. C53 | #21666 | semidirect |
| 196. C42 | #11719912 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133211 | 2 |
| #20275319 | 2 |
| #20275270 | 2 |
| #20274586 | 2 |
| #20274495 | 2 |
| C42×#88322 | 2 |
| C53×#1839 | 2 |
| #21666 | 53 |