Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
732 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 259 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. #20275272 | C2 | semidirect |
| 4. #20274858 | C2 | semidirect |
| 5. #20274589 | C2 | semidirect |
| 7. C42×C8×C53 | C2 | semidirect |
| 65. C42×C53 | M16 | semidirect |
| 99. C8×C53 | #126 | semidirect |
| 122. C42×C8 | D53 | semidirect |
| 144. C53 | #21666 | semidirect |
| 196. C42 | #11719912 | semidirect |
| 221. C8 | #13133211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13133211 | 2 |
| #20275321 | 2 |
| #20275272 | 2 |
| #20274858 | 2 |
| #20274589 | 2 |
| #20274498 | 2 |
| C42×C8×C53 | 2 |
| #21666 | 53 |