Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1708 conjugacy classes of subgroups; only the 288 normal subgroups are shown.
This group has 1708 conjugacy classes of subgroups — too many to draw. Only its 288 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. C24×#88324 | C2 | semidirect |
| 2. C2×#16811652 | C2 | semidirect |
| 3. #20290690 | C2 | semidirect |
| 4. #20290658 | C2 | semidirect |
| 5. #20290537 | C2 | semidirect |
| 6. #20290452 | C2 | semidirect |
| 8. C22×#11719936 | C22 | semidirect |
| 13. C2×C4⋊#88324 | C22 | semidirect |
| 14. C2×#13133274 | C22 | semidirect |
| 17. C2×#13133272 | C22 | semidirect |
| 18. #16811489 | C22 | semidirect |
| 31. C22×#88324 | D4 | semidirect |
| 60. C24×C53 | M16 | semidirect |
| 129. #88324 | #120 | semidirect |
| 136. C22×C53 | #435 | semidirect |
| 179. C53 | #21440 | semidirect |
| 215. C24 | #11719936 | semidirect |
| 292. C22 | #16811652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#88324 | 2 |
| C2×#16811652 | 2 |
| #20290690 | 2 |
| #20290658 | 2 |
| #20290537 | 2 |
| #20290452 | 2 |
| #20277214 | 2 |
| #21440 | 53 |