Finite Group DatabasebetaFinite Group DatabasebetaOrder 3072.
At least 7779 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has at least 7779 conjugacy classes of subgroups — too many to draw. Only its 174 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. C2×#11715661 | C2 | semidirect |
| 2. #72341492 | C2 | semidirect |
| 3. #72341452 | C2 | semidirect |
| 5. #11715661 | C22 | semidirect |
| 6. #11715657 | C22 | semidirect |
| 7. #11710937 | C4 | semidirect |
| 9. C2×#87548 | C4 | semidirect |
| 10. C2×#87547 | C4 | semidirect |
| 13. #87548 | C2×C4 | semidirect |
| 14. #87547 | C2×C4 | semidirect |
| 22. #63103 | Dic3 | semidirect |
| 24. C2×2−1+6 | Dic3 | semidirect |
| 25. C2×H(7,𝔽2) | Dic3 | semidirect |
| 52. C22×#41 | SL(2,ℤ/4) | semidirect |
| 54. C23×Q8 | SL(2,ℤ/4) | semidirect |
| 55. C23×D4 | SL(2,ℤ/4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11715661 | 2 |
| #72341492 | 2 |
| #72341452 | 2 |
| #72280922 | 3 |
| C2×#11710937 | 2 |
| #11712613 | 4 |